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The issue of testing two-dimensional iterative arrays with a constant number of test vectors independent of the array size (C-testability) is discussed in this paper. Sufficient conditions for C-testability are stated. It is shown that any two-dimensional array can be modified to become C-testable. An extension to systolic (synchronous) arrays is made. The approach simplifies testing systolic arrays by using one test vector to test many cells of the array in a periodic fashion. A two-dimensional array for matrix multiplication is used to illustrate the approach for systolic arrays.