In phase-shifting Fizeau interferometers, phase-shift errors and multiple-beam interference are the most common sources of systematic error affecting high-precision phase measurements. Nonsinusoidal waveforms can be minimized by applying synchronous detection with more than four samples. However, when phase-shift calibration is inaccurate, these algorithms cannot eliminate the effects of nonsinusoidal characteristics. Moreover, when measuring the surface profile of highly reflective samples, the calculated phase is critically determined not only by the decrease in the fringe contrast, but also by the coupling error between the harmonics and phase-shift errors. In this study, we calculate phase errors using phase-shifting algorithms that take into account the coupling error. We show that the 4N – 3 algorithm, which consists of a polynomial window function and a discrete Fourier transform term, results in the smallest phase error. As a demonstration, the surface profile of a highly reflective silicon wafer is measured using a wavelength-tuning Fizeau interferometer and the 4N – 3 algorithm.