Effective utilization of communication resources is crucial for improving performance in multiprocessor/communication systems. In this paper, the mutually independent hamiltonicity is addressed for its effective utilization of resources on the binary wrapped butterfly graph. Let be a graph with vertices. A hamiltonian cycle of is represented by to emphasize the order of vertices on . Two hamiltonian cycles of , namely and , are said to be independent if and for all . A collection of hamiltonian cycles , starting from the same vertex, are -mutually independent if any two different hamiltonian cycles are independent. The mutually independent hamiltonicity of a graph , denoted by , is defined to be the maximum integer such that, for each vertex of , there exists a set of -mutually independent hamiltonian cycles starting from . Let denote the -dimensional binary wrapped butterfly graph. Then we prove that for all .