In this paper, we present a new and efficient parallel algorithm for the solution of linear equations based on Householder reductions, Unlike the existing methods, the new algorithm integrates both triangula-tion and back substitution phases, and replaces the back substitution phase by only one step division. Further, being based on the Householder method, it has unconditional numerical stability. We present a scheduling scheme for assigning the computational tasks in the algorithm onto processors for efficient implementation ( of the algorithm) on multiprocessor systems. Also, we discuss the error analysis and the performance of the algorithm on hypercube multiprocessor systems.