diff --git a/Eigen/src/Sparse/TriangularSolver.h b/Eigen/src/Sparse/TriangularSolver.h
index 8948ae45e..390d0174b 100644
--- a/Eigen/src/Sparse/TriangularSolver.h
+++ b/Eigen/src/Sparse/TriangularSolver.h
@@ -43,8 +43,11 @@ struct ei_solve_triangular_selector<Lhs,Rhs,LowerTriangular,RowMajor|IsSparse>
         {
           lastVal = it.value();
           lastIndex = it.index();
+          if(lastIndex == i)
+            break;
           tmp -= lastVal * other.coeff(lastIndex,col);
         }
+
         if (Lhs::Flags & UnitDiagBit)
           other.coeffRef(i,col) = tmp;
         else
diff --git a/test/sparse_solvers.cpp b/test/sparse_solvers.cpp
index 8ce4e2264..3d7f5b91e 100644
--- a/test/sparse_solvers.cpp
+++ b/test/sparse_solvers.cpp
@@ -68,12 +68,20 @@ template<typename Scalar> void sparse_solvers(int rows, int cols)
     VERIFY_IS_APPROX(refMat2.template marked<LowerTriangular>().solveTriangular(vec2),
                      m2.template marked<LowerTriangular>().solveTriangular(vec3));
 
+    // lower - transpose
+    initSparse<Scalar>(density, refMat2, m2, ForceNonZeroDiag|MakeLowerTriangular, &zeroCoords, &nonzeroCoords);
+    VERIFY_IS_APPROX(refMat2.template marked<LowerTriangular>().transpose().solveTriangular(vec2),
+                     m2.template marked<LowerTriangular>().transpose().solveTriangular(vec3));
+
     // upper
     initSparse<Scalar>(density, refMat2, m2, ForceNonZeroDiag|MakeUpperTriangular, &zeroCoords, &nonzeroCoords);
     VERIFY_IS_APPROX(refMat2.template marked<UpperTriangular>().solveTriangular(vec2),
                      m2.template marked<UpperTriangular>().solveTriangular(vec3));
 
-    // TODO test row major
+    // upper - transpose
+    initSparse<Scalar>(density, refMat2, m2, ForceNonZeroDiag|MakeUpperTriangular, &zeroCoords, &nonzeroCoords);
+    VERIFY_IS_APPROX(refMat2.template marked<UpperTriangular>().transpose().solveTriangular(vec2),
+                     m2.template marked<UpperTriangular>().transpose().solveTriangular(vec3));
   }
 
   // test LLT