Transformation of square pulse signals by the multilayer Rosen type piezoelectric transformer (PT) is investigated with the goals to preserve the signal waveform and achieve maximum efficiency for power electronics and LED lighting applications. The voltage gain of the transformer is calculated from equations of linear piezoelectricity and motion for a broad frequency range that includes multiple resonant frequencies of PT. The transformation of the square pulse is simulated numerically by applying the voltage gain function to the Fourier spectrum of the input signal, and then restoring the time domain output signal from its spectrum. A half bridge MOSFET amplifier is built to drive the PT in the experimental setup. The measurements of the input and output waveforms and their Fourier spectra verify the calculations. It is shown that the components of the spectrum and the waveform of the square pulse signal can be preserved in the output signal by using multiple resonant frequencies of the transformer. With the accurate match between the signal harmonics and the resonant frequencies of the transformer voltage gain, the square pulse signal provides higher output power than a sine or a square wave, provided that the dominant harmonics of all signals have the same amplitude.