We present a new subexponential algorithm for computing the endomorphism ring of an ordinary abelian surface over a finite field which generalizes an algorithm of Bisson and Sutherland for elliptic curves. The correctness of this algorithm only requires GRH and a smoothness assumption on the norms of ideals, thus avoiding the multiple heuristic assumptions on isogeny graphs and polarized class groups which were previously required. Additionally, the output of the algorithm is much simpler than previous algorithms.