Memory cores are usually the densest portion with the smallest feature size in system-on-chip (SOC) designs. The reliability of memory cores thus has heavy impact on the reliability of SOCs. Transparent test is one of useful technique for improving the reliability of memories during life time. This paper presents a systematic algorithm used for transforming a bit-oriented march test into a transparent word-oriented march test. The transformed transparent march test has shorter test complexity compared with that proposed in the previous works [Theory of transparent BIST for RAMs, A transparent online memory test for simultaneous detection of functional faults and soft errors in memories]. For example, if a memory with 32-bit words is tested with March C-, time complexity of the transparent word-oriented test transformed by the proposed scheme is only about 56% or 19% time complexity of the transparent word-oriented test converted by the scheme reported in [Theory of transparent BIST for RAMs] or [A transparent online memory test for simultaneous detection of functional faults and soft errors in memories], respectively.