  We study precise calculation of neutralino relic density in the minimal
supergravity model. We compare the exact formula for the thermal average of the
neutralino annihilation cross section times relative velocity with the
expansion formula in terms of the temperature, including all the contributions
to neutralino annihilation cross section analytically. We confirm that the
expansion formula fails badly near s-channel poles. We show that the expansion
method causes 5-10 % error even far away from the poles.
