It is a long-standing and remarkable problem as to when and how red S0 galaxies were formed in clusters of galaxies. We here propose that the major mechanism for the S0 creation is galaxy merging between two spirals with unequal mass. Our numerical simulations demonstrate that galaxy merging exhausts a large amount of the interstellar medium of two gas-rich spirals, owing to the moderately enhanced star formation, and subsequently transforms the two into one gas-poor S0 galaxy with a structure and kinematics strikingly similar to the observed ones. This secondary S0 formation with enhanced star formation explains the smaller fraction of the S0 population recently observed in some distant clusters of galaxies. Unequal-mass galaxy mergers thus provide an evolutionary link between a larger number of blue spirals observed in intermediate- redshift clusters and the red S0's prevalent in the present-day ones.