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This paper presents a systematic procedure for transforming a bit-oriented March test into a transparent word-oriented March test. The test-time complexity of the transparent word-oriented March tests converted by the proposed method is only (P + 5 log2 B + 2)N for an N x B-bit Random Access Memory, and the test-time complexity of the corresponding signature-prediction test is QN. Here, P and Q denote the number of total Read/Write and Read test operations of the original bit-oriented March test. A transparent-test methodology for memories with error-correction code (ECC) is also proposed. This methodology can test and locate faulty cells, and no signature prediction is needed. The test-time complexity of the proposed transparent-test methodology for memories with ECC is only (P + 5 log2 B + 2) N.