diff --git a/Eigen/src/QR/Tridiagonalization.h b/Eigen/src/QR/Tridiagonalization.h
index 599786302..9ea39be71 100644
--- a/Eigen/src/QR/Tridiagonalization.h
+++ b/Eigen/src/QR/Tridiagonalization.h
@@ -201,6 +201,7 @@ void Tridiagonalization<MatrixType>::_compute(MatrixType& matA, CoeffVectorType&
     // squared norm of the vector v skipping the first element
     RealScalar v1norm2 = matA.col(i).end(n-(i+2)).squaredNorm();
 
+    // FIXME comparing against 1
     if (ei_isMuchSmallerThan(v1norm2,static_cast<Scalar>(1)))
     {
       hCoeffs.coeffRef(i) = 0.;
@@ -331,7 +332,8 @@ void Tridiagonalization<MatrixType>::_compute(MatrixType& matA, CoeffVectorType&
     if (ei_real(v0)>=0.)
       beta = -beta;
     matA.col(i).coeffRef(i+1) = beta;
-    hCoeffs.coeffRef(i) = (beta - v0) / beta;
+    if(ei_isMuchSmallerThan(beta, Scalar(1))) hCoeffs.coeffRef(i) = Scalar(0);
+    else hCoeffs.coeffRef(i) = (beta - v0) / beta;
   }
   else
   {