An assembly line with no paralleling of work elements and work stations is called a serial line. The cycle time of the serial line must be at least equal to the maximum work element time. To lower the cycle time beyond the limit and increase the production rate, one may permit the paralleling of work elements or work stations. So in this paper we propose the parallel assignment method for achieving a higher production rate. In this method, work elements are assigned to work stations under the multiple upper time limits which are the products of the various numbers of workers and the limiting cycle time. Further we develop the computer program of the proposed method and provide an illustrative problem and computational results.