Abstract The full array of the Large High Altitude Air Shower Observatory (LHAASO) has been in operation since July 2021. For its kilometer-square array (KM2A), we optimized the selection criteria for very high and ultra-high energy γ-rays using data collected from August 2021 to August 2022, resulting in an improvement in significance of the detection in the Crab Nebula of approximately 15%, compared with that of previous cuts. With the implementation of these new selection criteria, the angular resolution was also significantly improved by approximately 10% at tens of TeV. Other aspects of the full KM2A array performance, such as the pointing error, were also calibrated using the Crab Nebula. The resulting energy spectrum of the Crab Nebula in the energy range of 10-1000 TeV are well fitted by a log-parabola model, which is consistent with the previous results from LHAASO and other experiments.