diff --git a/Eigen/src/SVD/JacobiSVD.h b/Eigen/src/SVD/JacobiSVD.h
index 44beaf1c0..a0e8cf27a 100644
--- a/Eigen/src/SVD/JacobiSVD.h
+++ b/Eigen/src/SVD/JacobiSVD.h
@@ -694,16 +694,6 @@ JacobiSVD<MatrixType, QRPreconditioner>::compute(const MatrixType& matrix, unsig
   /*** step 2. The main Jacobi SVD iteration. ***/
   RealScalar maxDiagEntry = m_workMatrix.cwiseAbs().diagonal().maxCoeff();
 
-  // For a 1x1 complex matrix this boils down in cancelling the imaginary part
-  // This needs to be done explicitly because the "svd_precondition_2x2_block_to_be_real"
-  // wont't be applied as there is no 2x2 blocks!
-  if(NumTraits<Scalar>::IsComplex && m_diagSize==1 && abs(numext::imag(m_workMatrix.coeff(0,0)))>considerAsZero)
-  {
-    RealScalar z = abs(m_workMatrix.coeff(0,0));
-    if(computeU()) m_matrixU.col(0) *= m_workMatrix.coeff(0,0)/z;
-    m_workMatrix.coeffRef(0,0) = z;
-  }
-
   bool finished = false;
   while(!finished)
   {
@@ -748,10 +738,22 @@ JacobiSVD<MatrixType, QRPreconditioner>::compute(const MatrixType& matrix, unsig
 
   for(Index i = 0; i < m_diagSize; ++i)
   {
-    // At this stage, m_workMatrix.coeff(i,i) is supposed to be real.
-    RealScalar a = numext::real(m_workMatrix.coeff(i,i));
-    m_singularValues.coeffRef(i) = abs(a);
-    if(computeU() && (a<RealScalar(0))) m_matrixU.col(i) = -m_matrixU.col(i);
+    // For a complex matrix, some diagonal coefficients might note have been
+    // treated by svd_precondition_2x2_block_to_be_real, and the imaginary part
+    // of some diagonal entry might not be null.
+    if(NumTraits<Scalar>::IsComplex && abs(numext::imag(m_workMatrix.coeff(i,i)))>considerAsZero)
+    {
+      RealScalar a = abs(m_workMatrix.coeff(i,i));
+      m_singularValues.coeffRef(i) = abs(a);
+      if(computeU()) m_matrixU.col(i) *= m_workMatrix.coeff(i,i)/a;
+    }
+    else
+    {
+      // m_workMatrix.coeff(i,i) is already real, no difficulty:
+      RealScalar a = numext::real(m_workMatrix.coeff(i,i));
+      m_singularValues.coeffRef(i) = abs(a);
+      if(computeU() && (a<RealScalar(0))) m_matrixU.col(i) = -m_matrixU.col(i);
+    }
   }
   
   m_singularValues *= scale;