diff --git a/src/BOPAlgo/BOPAlgo_PaveFiller_6.cxx b/src/BOPAlgo/BOPAlgo_PaveFiller_6.cxx
index 2ed55c8b34..528e8a4a1e 100644
--- a/src/BOPAlgo/BOPAlgo_PaveFiller_6.cxx
+++ b/src/BOPAlgo/BOPAlgo_PaveFiller_6.cxx
@@ -1573,41 +1573,70 @@ void BOPAlgo_PaveFiller::RemoveUsedVertices(BOPDS_Curve& aNC,
                                           const Standard_Integer iCheckExtend)
 {
   Standard_Boolean bIsVertexOnLine;
-  Standard_Real aT, aTol, aTolNew;
-  BOPDS_Pave aPave;
+  Standard_Real aT, aTolV;
   //
-  const TopoDS_Vertex aV = (*(TopoDS_Vertex *)(&myDS->Shape(nV)));
+  const TopoDS_Vertex& aV = (*(TopoDS_Vertex *)(&myDS->Shape(nV)));
   Handle(BOPDS_PaveBlock)& aPB=aNC.ChangePaveBlock1();
   const IntTools_Curve& aIC = aNC.Curve();
   //
   bIsVertexOnLine=myContext->IsVertexOnLine(aV, aIC, aTolR3D, aT);
   if (!bIsVertexOnLine && iCheckExtend) {
-    aTol = BRep_Tool::Tolerance(aV);
+    aTolV = BRep_Tool::Tolerance(aV);
     //
-    ExtendedTolerance(nV, aMI, aTol, iCheckExtend);
-    bIsVertexOnLine=myContext->IsVertexOnLine(aV, aTol, aIC, aTolR3D, aT);
+    ExtendedTolerance(nV, aMI, aTolV, iCheckExtend);
+    bIsVertexOnLine=myContext->IsVertexOnLine(aV, aTolV, aIC, aTolR3D, aT);
   }
   //
   if (bIsVertexOnLine) {
-    aPave.SetIndex(nV);
-    aPave.SetParameter(aT);
+    // check if aPB contains the parameter aT
+    Standard_Boolean bExist;
+    Standard_Integer nVToUpdate;
+    Standard_Real aPTol, aDist, aTolVNew, aTolV2, aDTol;
+    TopoDS_Vertex aVToUpdate;
+    gp_Pnt aP1, aP2;
     //
-    aPB->AppendExtPave(aPave);
+    aTolV2 = 0.;
+    aDTol = 1.e-12;
     //
-    aTol = BRep_Tool::Tolerance(aV);
+    GeomAdaptor_Curve aGAC(aIC.Curve());
+    aPTol = aGAC.Resolution(aTolR3D);
     //
-    BOPTools_AlgoTools::UpdateVertex (aIC, aT, aV);
-    //
-    if (!aMVTol.IsBound(nV)) {
-      aTolNew = BRep_Tool::Tolerance(aV);
-      if (aTolNew > aTol) {
-        aMVTol.Bind(nV, aTol);
-      }
+    bExist = aPB->ContainsParameter(aT, aPTol, nVToUpdate);
+    if (bExist) {
+      // use existing pave
+      aP1 = BRep_Tool::Pnt(aV);
+      aTolV2 = BRep_Tool::Tolerance(aV);
+      aVToUpdate = (*(TopoDS_Vertex *)(&myDS->Shape(nVToUpdate)));
+    }
+    else {
+      // add new pave
+      BOPDS_Pave aPave;
+      aPave.SetIndex(nV);
+      aPave.SetParameter(aT);
+      aPB->AppendExtPave(aPave);
+      //
+      aP1 = aGAC.Value(aT);
+      nVToUpdate = nV;
+      aVToUpdate = aV;
+    }
+    //
+    aTolV = BRep_Tool::Tolerance(aVToUpdate);
+    aP2 = BRep_Tool::Pnt(aVToUpdate);
+    aDist = aP1.Distance(aP2);
+    aTolVNew = aDist - aTolV2;
+    //
+    if (aTolVNew > aTolV) {
+      BRep_Builder aBB;
+      aBB.UpdateVertex(aVToUpdate, aTolVNew+aDTol);
+      //
+      if (!aMVTol.IsBound(nVToUpdate)) {
+        aMVTol.Bind(nVToUpdate, aTolV);
+      }
+      // 
+      BOPDS_ShapeInfo& aSIDS=myDS->ChangeShapeInfo(nVToUpdate);
+      Bnd_Box& aBoxDS=aSIDS.ChangeBox();
+      BRepBndLib::Add(aVToUpdate, aBoxDS);
     }
-    // 
-    BOPDS_ShapeInfo& aSIDS=myDS->ChangeShapeInfo(nV);
-    Bnd_Box& aBoxDS=aSIDS.ChangeBox();
-    BRepBndLib::Add(aV, aBoxDS);
   }
 }
 
@@ -2001,7 +2030,7 @@ void BOPAlgo_PaveFiller::UpdatePaveBlocks(const BOPCol_DataMapOfIntegerInteger&
         }
         //
         if (bRebuild) {
-          nSp = SplitEdge(aPB->Edge(), nV[0], aT[0], nV[1], aT[1]);
+          nSp = SplitEdge(aPB->OriginalEdge(), nV[0], aT[0], nV[1], aT[1]);
           if (bCB) {
             aCB->SetEdge(nSp);
           }
diff --git a/src/BOPAlgo/BOPAlgo_PaveFiller_8.cxx b/src/BOPAlgo/BOPAlgo_PaveFiller_8.cxx
index 124490bb21..7bad8897ec 100644
--- a/src/BOPAlgo/BOPAlgo_PaveFiller_8.cxx
+++ b/src/BOPAlgo/BOPAlgo_PaveFiller_8.cxx
@@ -244,7 +244,7 @@ static
                                      const Handle(BOPDS_PaveBlock)& aPBD)
 {
   Standard_Boolean bXDir, bIsDone, bReject;
-  Standard_Integer nE, aNbPoints, j;
+  Standard_Integer nE, aNbPoints, j, anInd;
   Standard_Real aTD1, aTD2, aT1, aT2, aTolInter, aX, aDT;
   Standard_Real aTolCmp;
   gp_Pnt2d aP2d1, aP2d2, aP2D;
@@ -330,7 +330,7 @@ static
       }
       //
       bReject=Standard_False;
-      if (aPBD->ContainsParameter(aX, aDT)) {
+      if (aPBD->ContainsParameter(aX, aDT, anInd)) {
         continue;
       }
       aPave.SetParameter(aX);
diff --git a/src/BOPDS/BOPDS_PaveBlock.cdl b/src/BOPDS/BOPDS_PaveBlock.cdl
index 385c936583..48aba298e1 100644
--- a/src/BOPDS/BOPDS_PaveBlock.cdl
+++ b/src/BOPDS/BOPDS_PaveBlock.cdl
@@ -186,13 +186,15 @@ is
 	 
     ContainsParameter(me; 
         thePrm:Real from Standard; 
-        theTol:Real from Standard) 
+        theTol:Real from Standard;
+        theInd:out Integer from Standard) 
     returns Boolean from Standard; 
     ---Purpose: 
     --- Query 
     --- Returns true if the extra paves contain the pave 
     --- with given value of the parameter <thePrm> 
     ---  <theTol>  - the value of the tolerance to compare 
+    ---  <theInd>  - the Index of the found pave
  
     -- 
     -- shrunk data   
diff --git a/src/BOPDS/BOPDS_PaveBlock.cxx b/src/BOPDS/BOPDS_PaveBlock.cxx
index f75bac17ec..d3c09e3209 100644
--- a/src/BOPDS/BOPDS_PaveBlock.cxx
+++ b/src/BOPDS/BOPDS_PaveBlock.cxx
@@ -234,21 +234,19 @@ static
 //purpose  : 
 //=======================================================================
   Standard_Boolean BOPDS_PaveBlock::ContainsParameter(const Standard_Real theT,
-                                                      const Standard_Real theTol)const
+                                                      const Standard_Real theTol,
+                                                      Standard_Integer& theInd) const
 {
   Standard_Boolean bRet;
-  Standard_Real dT;
   BOPDS_ListIteratorOfListOfPave aIt;
   //
-  bRet=Standard_False;
+  bRet = Standard_False;
   aIt.Initialize(myExtPaves);
   for (; aIt.More(); aIt.Next()) {
-    dT=aIt.Value().Parameter()-theT;
-    if (dT<0.) {
-      dT=-dT;
-    }
-    if (dT<theTol) {
-      bRet=!bRet;
+    const BOPDS_Pave& aPave = aIt.Value();
+    bRet = (Abs(aPave.Parameter() - theT) < theTol);
+    if (bRet) {
+      theInd = aPave.Index();
       break;
     }
   }
diff --git a/tests/bugs/modalg_6/bug26444 b/tests/bugs/modalg_6/bug26444
new file mode 100644
index 0000000000..c873f15bcf
--- /dev/null
+++ b/tests/bugs/modalg_6/bug26444
@@ -0,0 +1,17 @@
+puts "========"
+puts "OCC26444"
+puts "========"
+puts ""
+####################################################################################
+# Boolean operation "bcut" gives invalid result between solid and halfspace solid.
+####################################################################################
+
+restore [locate_data_file bug26444_cutting_shape.brep] a
+restore [locate_data_file bug26444_shape_to_cut.brep] b
+restore [locate_data_file bug26444_ref_out.brep] p2
+dump p2
+halfspace s1 a -0.541421905726473 0.200000002980232 0.00899999961256981
+bcut result b s1
+
+set square 0.106547
+set 2dviewer 1