Let G=(V,E) be a graph of order n. A Hamiltonian cycle of G is a cycle that contains every vertex in G. Two Hamiltonian cycles C₁=<u₁,u₂,…,u_n,u₁> and C₂=<v₁,v₂,…,v_n,v₁> of G are independent if u₁=v₁ and u_i≠v_i for 2≤i≤n. A set of Hamiltonian cycles {C₁,C₂,…,C_k} of G is mutually independent if its elements are pairwise independent. The mutually independent hamiltonicity IHC(G) of a graph G is the maximum integer k such that for any vertex u of G there are k mutually independent Hamiltonian cycles of G starting at u. For the n-dimensional burnt pancake graph B_n, this paper proved that IHC(B₂)=1 and IHC(B_n)=n for n≥3.