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We revisit the evolution of galaxy morphology in the COSMOS field over theredshift range $0.2\leq z \leq 1$, using a large and complete sample of 33,605galaxies with a stellar mass of log($M_{\ast}$/M$_{\odot} )>9.5$ withsignificantly improved redshifts and comprehensive non-parametric morphologicalparameters. Our sample has 13,881 ($\sim41.3\%$) galaxies with reliablespectroscopic redshifts and has more accurate photometric redshifts with a$\sigma_{\rm NMAD} \sim 0.005$. This paper is the first in a series thatinvestigates merging galaxies and their properties. We identify 3,594 majormerging galaxies through visual inspection and find 1,737 massive galaxy pairswith log($M_\ast$/M$_\odot$)$>10.1$. Among the family of non-parametricmorphological parameters including $C$, $A$, $S$, $Gini$, $M_{\rm 20}$, $A_{\rmO}$, and $D_{\rm O}$, we find that the outer asymmetry parameter $A_{\rm O}$and the second-order momentum parameter $M_{\rm 20}$ are the best tracers ofmerging features than other combinations. Hence, we propose a criterion forselecting candidates of violently star-forming mergers: $M_{\rm 20}> -3A_{\rmO}+3$ at $0.2<z<0.6$ and $M_{\rm 20}> -6A_{\rm O}+3.7$ at $0.6<z<1.0$.Furthermore, we show that both the visual merger sample and the pair sampleexhibit a similar evolution in the merger rate at $z<1$, with $\Re\sim(1+z)^{1.79 \pm 0.13}$ for the visual merger sample and $\Re\sim(1+z)^{2.02\pm 0.42}$ for the pair sample. The visual merger sample has aspecific star formation rate that is about 0.16\,dex higher than that ofnon-merger galaxies, whereas no significant star formation excess is observedin the pair sample. This suggests that the effects of mergers on star formationdiffer at different merger stages.

Revisiting Galaxy Evolution in Morphology in the COSMOS field (COSMOS-ReGEM):I. Merging Galaxies