We present a new scenario for the origin of the counter-rotating stars in disc galaxies, defined as stars that have a negative tangential velocity. This scenario involves a merger between two gas-rich disc galaxies that have comparable masses, are nearly co-planar, and are rotating in the same direction. The merger results in an intense starburst, during which a significant fraction of the gas is converted to stars. The system then settles into an equilibrium configuration consisting of a thick disc and a bulge partly supported by velocity dispersion and a thin disc supported by rotation. Star formation proceeds until most of the gas supply is exhausted. Stars formed during the starburst have tangential velocities ranging from −600 km s−1 to 600 km s−1. Stars formed afterward in the thick disc and bulge have high eccentricities and low tangential velocities, typically in the range −100 km s−1 to 100 km s−1, while stars formed in the thin disc have large, positive velocities. All fast, counter-rotating stars (V < −200 km s−1) are old, metal-poor, with very low dispersion in ages and metallicities. By contrast, fast, co-rotating stars (V > 200 km s−1) have a wide range of ages and metallicities. The average abundances ratios $\rm [O/H]$ and [Fe/H] for fast, co-rotating stars typically exceed the corresponding ratios for fast, counter-rotating stars by 0.1 dex to 0.4 dex, while the dispersion in the values of NFe/NH are larger by factors between 2 and 14. This provides an observational signature of major, gas-rich mergers at high redshift.