The degree of randomness of higher order than first order was proposed to characterize the alternating structure of binary copolymers. The introduced parameter describes the alternating structure more precisely than the degree of alternation already proposed in the literature. Furthermore, the new parameter can be used in connection with standard copolymerization models where the need for such parameters is especially high. In this domain the degree of alternation fails. The usefulness of the degree of randomness was tested on model chains and two standard copolymerization models : the terminal and simplified penultimate model. This examination proves that more precise information on comonomer sequencing can be obtained when sequences longer than diads are described by means of the degree of randomness.