An improved theory for the input impedance of a probe-fed microstrip patch antenna has been developed. The natural modes are established on a transverse resonance condition which incorporates the angularly dependent reflection coefficients and a dynamic wall susceptance associated with the patch boundaries. The input reactance is shown to be largely associated with the evanescent waves confined to the vicinity of the probe while the input resistance is associated with the excitation of the mode at resonance. Analytical results are presented to describe the input impedance of a rectangular patch antenna as a function of its dimensions, substrate thickness and dielectric constant, probe dimensions and location and the frequency.