A hamiltonian cycle C of G is described as \left\langle {\mu _1 ,\mu _2 ,....,\mu _n (G),\mu _1 )} \right\rangle to emphasize the order of nodes in C. Thus, \mu _1 is the beginning node and ui is the i-th node in C. Two hamiltonian cycles of G beginning at u, C1 = \left\langle {\mu _1 ,\mu _2 ,....,\mu _n (G),\mu _1 )} \right\rangle and C2 = \left\langle {\mu _1 ,\mu _2 ,....,\mu _n (G),\mu _1 )} \right\rangle , are independent if u = \mu _1 = \mu _1, and \mu _1 \ne \mu _1 for 1 \le i \le n(G). A set of hamiltonian cycles \{ C_1 ,C_2 ,...,C_k \} of G are mutually independent if any two different hamiltonian cycles are independent. The mutually independent hamiltonianicity of graph G, IHC(G), is the maximum integer k such that for any node u of G there exist k-mutually independent hamiltonian cycles of G starting at u. Let Q_n be the n-dimensional hypercube. We prove that IHC(Q_n) = n - 1 if n \in {1, 2, 3} and IHC(Q_n) = n if n \ge 4.