The two-dimensional hemispherical dynamo theory is based on the symmetry aboutthe equator, and has certain inherent theoretical shortcomings and limitations in application. In order to extend the dynamo theory to the globe, the assumption of thesymmetry about the equator is removed in present study, the boundary condition atthe north (or south) pole is also removed. In this way the conventional boundaryproblem becomes "boundary--free" one, which describes more reasonably the physicsof the dynamo process and would show some essential characteristics. For instance,this method can be used to study seasonal and UTvariations of the Sq
currentsystem, as well as dynamo effects of the non-dipole magnetic field, all of which areasymmetric about the equator. The global current system obtained by using presentmethod for simple symmetric condition is same as that by using hemispheric symmetric dynamo theory. As for asymmetric condition, the current intensity, focus location, current direction and other characteristics show more complicated features, whichcan not be explained by hemispheric dynamo theory.