March-series test algorithms have proven to be popular choices for Memory BIST implementation, owing to its simplicity yet having a good fault coverage. However, March test algorithms with low test complexities are incapable to detect some unlinked Single-Cell faults and many Double-Cell faults. This paper presents a new optimization strategy aimed to improve the fault coverage of the existing March test algorithms by detecting the previously undetectable Single-Cell faults and Double-Cell faults. It is achieved by optimizing the test operation sequences of the existing March test algorithms through an automation program, to achieve higher fault coverage while maintaining the same test complexity as the original March algorithm. Performance analysis shows that the fault coverage can be improved from 44% to 72% for March LR, by using the proposed optimization strategy.