Morphological classification conveys abundant information on the formation, evolution, and environment of galaxies. In this work, we refine a two-step galaxy morphological classification framework (USmorph), which employs a combination of unsupervised machine-learning and supervised machine-learning techniques, along with a self-consistent and robust data-preprocessing step. The updated method is applied to galaxies with Imag<25 at 0.2<z<1.2 in the COSMOS field. Based on their Hubble Space Telescope/Advanced Camera for Survey I-band images, we classify them into five distinct morphological types: spherical (SPH, 15200), early-type disk (17369), late-type disk (21143), irregular disk (IRR, 28965), and unclassified (UNC, 17129). In addition, we have conducted both parametric and nonparametric morphological measurements. For galaxies with stellar masses exceeding 10^9^M_{sun}_, a gradual increase in effective radius from SPHs to IRRs is observed, accompanied by a decrease in the Sersic index. Nonparametric morphologies reveal distinct distributions of galaxies across the Gini-M_20_ and C-A parameter spaces for different categories. Moreover, different categories exhibit significant dissimilarity in their G_2_ and {Psi} distributions. We find morphology to be strongly correlated with redshift and stellar mass. The consistency of these classification results with expected correlations among multiple parameters underscores the validity and reliability of our classification method, rendering it a valuable tool for future studies.