Summary: A 4-cycle system is said to be diagonally switchable if each 4-cycle can be replaced by another 4-cycle obtained by replacing one pair of non-adjacent edges of the original 4-cycle by its diagonals so that the transformed set of 4-cycles forms another 4-cycle system. The existence of diagonally switchable 4-cycle system of $K_v$ has already been solved [{\it P. Adams, D. Bryant, M. Grannell} and {\it T. Griggs}, Australas. J. Comb. 34, 145‒152 (2006; Zbl 1104.05015)]. In this paper we give an algernative proof of this result and use the method to prove a new result for $K_v-I$, where $I$ is any one factor of $K_v$.