A direct method for superresolution recently proposed by Walsh and Delaney is further analyzed from the point of view of numerical stability. The method is based on a set of linear equations Ax = b, where A is m × n, and b is a subset (of cardinal n) of the Fourier transform of the object (which has a total of N samples). We give exact and best possible approximate expressions for the determinant of A, when m = n. As a corollary, it is shown that the smallest eigenvalue of A in absolute value satisfies |λ min | ≤ k(n)N −(n−1)/2 , where k(n) (which is independent of N ) is explicitly given. The magnitude of the smallest eigenvalue of A becomes increasingly small as N grows, even when the number of unknowns n remains constant. When m > n the singular values of A are studied, and related to the eigenvalues of the matrix of two other direct methods. As a result, the connection between the method and the other direct methods is clarified.