A double-peak X-ray burst from the Galactic magnetar SGR J1935+ 2154 was discovered to be associated with the two radio pulses of FRB 200428 separated by 28.97±0.02 ms. Precise measurements of the timing and spectral properties of the X-ray bursts are helpful for understanding the physical origin of fast radio bursts. In this paper, we have reconstructed some information about the hard X-ray events, which were lost because the High Energy X-ray Telescope (HE) on board the Insight-HXMT mission was saturated by this extremely bright burst, and used the information to improve the temporal and spectral analyses of the X-ray burst. The arrival times of the two X-ray peaks by fitting the new Insight-HXMT/HE lightcurve with multi-Gaussian profiles are 2.77±0.45 ms and 34.30±0.56 ms after the first peak of FRB 200428, respectively, while these two parameters are 2.57±0.52 ms and 32.5±1.4 ms if the fitting profile is a fast-rise and exponential decay function. The spectrum of the two X-ray peaks could be described by a cutoff power law with cutoff energy∼ 60 keV and photon index∼ 1.4; the latter is softer than the result obtained in Li et al. when the two X-ray peaks appeared.