An efficient parallel algorithm, farmzeroinNR, for the eigenvalue problem of a symmetric tridiagonal matrix is implemented in a distributed memory multiprocessor with 112 nodes. The basis of our parallel implementation, is an improved version of the zeroinNR method. It is consistently faster than simple bisection and produces more accurate eigenvalues than the QR} method. As it happens with bisection, zeroinNR exhibits great flexibility and allows the computation of a subset of the spectrum with some prescribed accuracy. Results were carried out with matrices of different types and sizes up to $10^4$ and show that our algorithm is efficient and scalable.