The iterative aggregation method for the solution of a system of linear algebraic equations x = Ax + b, where A ≥ 0, b ≥ 0, s > 0, and s ′ A < s ′, is proved to be locally convergent. It is shown that the method can be considered a consistent nonstationary iterative method, where the iteration matrix depends on the current iterate, and that some norm of the iteration matrix is less than one in the vicinity of the solution.