diff --git a/Eigen/src/SparseCore/SparseTriangularView.h b/Eigen/src/SparseCore/SparseTriangularView.h
index 68c4c3397..88a345b22 100644
--- a/Eigen/src/SparseCore/SparseTriangularView.h
+++ b/Eigen/src/SparseCore/SparseTriangularView.h
@@ -2,6 +2,7 @@
 // for linear algebra.
 //
 // Copyright (C) 2009 Gael Guennebaud <gael.guennebaud@inria.fr>
+// Copyright (C) 2012 Désiré Nuentsa-Wakam <desire.nuentsa_wakam@inria.fr>
 //
 // This Source Code Form is subject to the terms of the Mozilla
 // Public License v. 2.0. If a copy of the MPL was not distributed
@@ -27,6 +28,7 @@ template<typename MatrixType, int Mode> class SparseTriangularView
     enum { SkipFirst = ((Mode&Lower) && !(MatrixType::Flags&RowMajorBit))
                     || ((Mode&Upper) &&  (MatrixType::Flags&RowMajorBit)),
            SkipLast = !SkipFirst,
+           SkipDiag = (Mode&ZeroDiag) ? 1 : 0,
            HasUnitDiag = (Mode&UnitDiag) ? 1 : 0
     };
 
@@ -71,7 +73,7 @@ class SparseTriangularView<MatrixType,Mode>::InnerIterator : public MatrixTypeNe
     {
       if(SkipFirst)
       {
-        while((*this) && (HasUnitDiag ? this->index()<=outer : this->index()<outer))
+        while((*this) && ((HasUnitDiag||SkipDiag)  ? this->index()<=outer : this->index()<outer))
           Base::operator++();
         if(HasUnitDiag)
           m_returnOne = true;
@@ -101,8 +103,8 @@ class SparseTriangularView<MatrixType,Mode>::InnerIterator : public MatrixTypeNe
       return *this;
     }
 
-    inline Index row() const { return Base::row(); }
-    inline Index col() const { return Base::col(); }
+    inline Index row() const { return (MatrixType::Flags&RowMajorBit ? Base::outer() : this->index()); }
+    inline Index col() const { return (MatrixType::Flags&RowMajorBit ? this->index() : Base::outer()); }
     inline Index index() const
     {
       if(HasUnitDiag && m_returnOne)  return Base::outer();
@@ -118,7 +120,12 @@ class SparseTriangularView<MatrixType,Mode>::InnerIterator : public MatrixTypeNe
     {
       if(HasUnitDiag && m_returnOne)
         return true;
-      return (SkipFirst ? Base::operator bool() : (Base::operator bool() && this->index() <= this->outer()));
+      if(SkipFirst) return  Base::operator bool();
+      else
+      {
+        if (SkipDiag) return (Base::operator bool() && this->index() < this->outer());
+        else return (Base::operator bool() && this->index() <= this->outer());
+      }
     }
   protected:
     bool m_returnOne;
@@ -134,9 +141,10 @@ class SparseTriangularView<MatrixType,Mode>::ReverseInnerIterator : public Matri
       : Base(view.nestedExpression(), outer)
     {
       eigen_assert((!HasUnitDiag) && "ReverseInnerIterator does not support yet triangular views with a unit diagonal");
-      if(SkipLast)
-        while((*this) && this->index()>outer)
+      if(SkipLast) {
+        while((*this) && (SkipDiag ? this->index()>=outer : this->index()>outer))
           --(*this);
+      }
     }
 
     EIGEN_STRONG_INLINE ReverseInnerIterator& operator--()
@@ -147,7 +155,12 @@ class SparseTriangularView<MatrixType,Mode>::ReverseInnerIterator : public Matri
 
     EIGEN_STRONG_INLINE operator bool() const
     {
-      return SkipLast ? Base::operator bool() : (Base::operator bool() && this->index() >= this->outer());
+      if (SkipLast) return Base::operator bool() ;
+      else
+      {
+        if(SkipDiag) return (Base::operator bool() && this->index() > this->outer());
+        else return (Base::operator bool() && this->index() >= this->outer());
+      }
     }
 };
 
diff --git a/test/sparse_basic.cpp b/test/sparse_basic.cpp
index 121cc05b1..2f92f1627 100644
--- a/test/sparse_basic.cpp
+++ b/test/sparse_basic.cpp
@@ -3,6 +3,7 @@
 //
 // Copyright (C) 2008-2011 Gael Guennebaud <gael.guennebaud@inria.fr>
 // Copyright (C) 2008 Daniel Gomez Ferro <dgomezferro@gmail.com>
+// Copyright (C) 2013 Désiré Nuentsa-Wakam <desire.nuentsa_wakam@inria.fr>
 //
 // This Source Code Form is subject to the terms of the Mozilla
 // Public License v. 2.0. If a copy of the MPL was not distributed
@@ -391,6 +392,14 @@ template<typename SparseMatrixType> void sparse_basic(const SparseMatrixType& re
     refMat3 = refMat2.template triangularView<UnitLower>();
     m3 = m2.template triangularView<UnitLower>();
     VERIFY_IS_APPROX(m3, refMat3);
+
+    refMat3 = refMat2.template triangularView<StrictlyUpper>();
+    m3 = m2.template triangularView<StrictlyUpper>();
+    VERIFY_IS_APPROX(m3, refMat3);
+
+    refMat3 = refMat2.template triangularView<StrictlyLower>();
+    m3 = m2.template triangularView<StrictlyLower>();
+    VERIFY_IS_APPROX(m3, refMat3);
   }
   
   // test selfadjointView
@@ -454,6 +463,14 @@ template<typename SparseMatrixType> void sparse_basic(const SparseMatrixType& re
           
       }
   }
+
+  // test Identity matrix
+  {
+    DenseMatrix refMat1 = DenseMatrix::Identity(rows, rows);
+    SparseMatrixType m1(rows, rows);
+    m1.setIdentity();
+    VERIFY_IS_APPROX(m1, refMat1);
+  }
 }
 
 void test_sparse_basic()