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We investigate the nonlocal advantage of quantum coherence (NAQC) and entanglement for two spins coupled via the Heisenberg interaction and under the intrinsic decoherence.Solutions of this decoherence model for the initial spin-1/2 and spin-1 maximally entangled states are obtained,based on which we calculate the NAQC and entanglement.In the weak region of magnetic field,the NAQC behaves as a damped oscillation with the time evolves,while the entanglement decays exponentially (behaves as a damped oscillation) for the spin-1/2 (spin-1) case.Moreover,the decay of both the NAQC and entanglement can be suppressed significantly by tuning the magnetic field and anisotropy of the spin interaction to some decoherence-rate-determined optimal values.