A new approximate form for the exchange-correlation energy functional is developed. The form is lased on the density matrix expansion (DME) for the exchange functional [R. M. Koehl, G. K. Odom, and G. E. Scuseria,Mol. Phys. 87, 835 (1996)]. The nonlocal portion of the correlation energy is assumed to have the same general form as that derived for exchange, while the local portion is taken to be that of the uniform electron gas. The resulting formula does not resort to the use of exact-exchange mixing. A Kohn-Sham implementation of this functional is constructed and the parameters within the functional are adjusted to minimize the difference between the theoretical and the experimental data for a large set of atomic and molecular systems. The results are found to compare favorably with existing functionals, even those which include exact-exchange mixing.