A new approach to automatically generating diagnostic memory tests of linear order (O(N)) is presented. The resulting March tests provide complete detection and distinguishing of all single-cell and two-cell fault models. The approach is based on state transition graph modelling, decomposition of functional memory faults into basic fault effects, and output tracing. For each of the targeted basic fault effects, all possible March sequences are generated. A fast greedy-based algorithm is then used to compose diagnostic March tests from the set of March sequences. The proposed test generation algorithm was implemented in C. The results show that automatic generation can compete with hand-optimization of diagnostic March tests.