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Soft decision decoding (SDD) provides a better coding gain by making use of the unquantized channel output. In this paper we introduce the concept of a Reliability Level List (RLL); based on the RLL a new SDD algorithm for Binary Phase Shift Keying (BPSK) based binary cyclic block codes is proposed. The algorithm guarantees to extract the most reliable codeword in an iterative manner. The formation of the RLL involves a search for the next possible entry into the RLL based on the error probability which is a reflection of the reliability values of the bits of the received word obtained from the channel. The procedure for the formation of RLL which is the central idea of the paper is given as a structured algorithm.