  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
have optimized the selection criteria for very high and ultra-high energy
$\gamma$-rays, using the data collected from August 2021 to August 2022,
resulting in an improvement on significance of about 15$\%$ compared with
previous cuts. With the implementation of these new selection criteria, the
angular resolution is also significantly improved by approximately 10$\%$ at
tens of TeV. Other aspects of the full KM2A array performance, such as the
pointing error are also calibrated using the Crab Nebula. The resulting energy
spectrum of the Crab Nebula in the energy range of 10-1000 TeV can be well
fitted by a log-parabola model, which is consistent with the previous results
from LHAASO and other experiments.
