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In this paper, we proposed a new scheme that supports micro mobility and macro mobility. By using this scheme, we do not have to communicate with the home agent of the mobile host when the mobile host moves from one MPLS subnet to another. Through simulations, we demonstrated that by using MINHM, we could provide lower end-to-end delay and delay jitter to the traffic during handoff periods. Thus, MINHM is a better approach to support smooth handoff in delay sensitive applications over conventional HIPv6 and conventional mobile MPLS. The scheme is based on the hierarchical mobile MPLS and extends hierarchical mobile MPLS. So it is better than hierarchical mobile MPLS, which is proposed in T. Yang and D. Makrakis (2001).