In physics, acceleration, velocity, and displacement should be convertible with each other. However, many strong-motion data do not meet this requirement; the double integration of a disseminated acceleration might not be the same as the corresponding disseminated displacement. This data incompatibility influences not only on the waveform but also on the derived terms from acceleration, such as response spectra. This can become a serious problem in the calculation of a nonlinear response (Pecknold and Riddell 1978, 1979). We show that the non-zero initial value of waveforms is the direct source of the dada incompatibility, and propose a numerical algorithm to solve the problem by adding a prefix acceleration impulse. We suggest a polynomial function of order of three as the impulse function. The coefficients of this polynomial function can be determined by initial acceleration, velocity and displacement which can be obtained by routine data processing. Numerical tests show this added impulse can effectively remove the data incompatibility and cause negligible effects on waveforms and response spectra.