The procedure of a quantum measurement, the unambiguous state discrimination, is studied for the case of four two-mode coherent states of the optical field, interesting for information transmission via an optical communication channel. It is shown that a complex conjugation of the amplitude of one of the modes results in a better distinguishability of the states. An interferometric scheme is suggested for unambiguous discrimination of such states and the probability of successful discrimination is found. Applications of the considered state set are discussed for quantum cryptography, quantum teleportation and optical communications with a high level of loss.