Recently there has been a renewed interest in finding reliable methods for reducing general matrices to tridiagonal form. We haave developed a serial reduction algorithm that appears to be very reliable in practice by incorporating in optimal pivot search and two recovery schemes. In this paper we describe a parallel version of our algorithm. HTe algorithm was developed as one step in the process of finding eigenvalues of non symmetric matrices. Our original parallel eigenvalue routines reduced the matrix to tridigonal form and the algorithms with our previous parallel algorihm and show that the new algorithm is nearly an order of magnitude faster, allowing us to be solve much larger problems than previously attempted