An angular measuring system is the most important component of high-precision test turntables; its function and precision determine the turntable's function and precision. The angular measuring system's error was considered as a stationary signal in the past. An autocorrelation function and spectrum characteristics of the angular measuring system error are analyzed using the cyclostationary signal theory. The idea that the error in the angular measuring system is nonstationary is first put forward; theory is provided to reconstruct the angular measuring system's error signal using wavelet analysis. The error signal is reconstructed using one-dimensional Mallat's algorithm. The standard deviation between the reconstructed and the original signal is much less than the angular measuring system's accuracy. The reconstruction signal is used to compensate the system error instead of the original error signal; the angular measuring system accuracy is improved.