This paper presents a new write latency reduction scheme for a Phase Change Memory (PCM) made of Multi-Level Cells (MLCs). This scheme improves over an existing scheme found in the technical literature and known as CABS. The proposed scheme is based on the utilization of a new coding arrangement for the selection of candidate codewords. The code relies on the two-step feature found in the write operation of a MLC PCM and avoids the symbol that incurs in the largest latency at a higher rate than CABS. A detailed simulation based evaluation and comparison are also pursued; the proposed scheme accomplishes improvements in write latency (for parallel writing) as well as coding rate (16/17 for the proposed scheme versus 16/18 for CABS for 16 symbols or 32-bit word). As the proposed scheme utilizes novel selection criteria for the candidates, the design of the required circuitry (encoder and decoder) has also been changed with respect to CABS; in terms of hardware, the areas of the encoder and decoder for the proposed scheme are reduced by 73 and 56 percent respectively compared with CABS.