Finding the error locator polynomial for decoding is achieved by several algorithms, such as the Peterson-Gorenstein-Zierler (PGZ) algorithm and the Berlekamp-Massey (BM) algorithm. This paper presents a two-stage decoding method for BCH codes using both algorithms. First, we run the first-stage PGZ algorithm implemented in parallel for fast decoding. Since the PGZ algorithm is not feasible for large numbers of errors, the correction capability of the first stage is limited. When such errors occur, the computation of the previous PGZ algorithm is recycled for the second-stage BM algorithm. In other words, we study a relay method to convert failed results of the PGZ algorithm to parameters of the subsequent BM algorithm. Our relay method using the PGZ algorithm is easier to select the relayed parameters than an unfolding of the BM algorithm using a binary decision tree. Using the relayed parameters removes several iterative updates of the subsequent BM algorithm, so that our relay algorithm can be a quick and simple start for fast decoding.