A northward component of the earth's rotation (b-effect) is included in a set of linearized, non-hydrostatic equations to study symmetric instability. The results show that the b-effect can be important if the perturbations are functions of the latitude. In comparison with the conventional symmetric instability, results also show that, in the northern hemisphere, when the temperature increases with latitude, the growth rate can be enhanced by the b-effect, and the growth rate decreases when the temperature decreases with latitude. We also find that when the perturbations are independent of latitude, the b-effect disappears. The physical explanation is provided.