The variation of the size and position of a parasitic element with the input impedance and bandwidth of a stack rectangular microstrip antenna is investigated theoretically. An integral equation for the unknown patch current densities is formulated in the spectral domain. The Galerkin procedure is employed to solve for the solution. It is found that the input impedance varies significantly with the size and position of the parasitic patch. The result is important for bandwidth enhancement and impedance matching of the microstrip antenna.