Convergence with probability 1 of the sign-sign algorithm with a decreasing step size is proven when it is used in adaptive plant identification. The plant input and plant noise are assumed stationary and M-dependent. The assumptions do not pose any upper bound on the memory, M, of the plant input and plant noise, and hence, they allow arbitrarily strong correlation in these signals. A main interest of the paper is that it provides a condition of persistent excitation of the algorithm. Examples satisfying this condition are provided.