Assume that m and n are positive even integers with n ≥ 4. The honeycomb rectangular torus HReT(m, n) is recognized as another attractive alternative to existing torus interconnection networks in parallel and distributed applications. It is known that any HReT(m, n) is a 3-regular bipartite graph. We prove that any HReT(m, n) - e is hamiltonian for any edge eE(HReT(m, n)). Moreover, any HReT(m, n) - F is hamiltonian for any F = (a, b) with a ∈ A and b ∈ B where A and B are the bipartition of HReT(m, n), if n ≥ 6 or m = 2.