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Building heterogeneous multi-core processor is desirable because it may provide high parallel performance such as instruction level parallelism (ILP) and thread-level parallelism (TLP). However, most existing operating system and parallel applications can't make good use of this heterogeneity because it arises dramatic instability sometimes, especially when the work of different core is unbalanced. In this paper we design a non-monotonic architecture consisted of two different types of cores to avoid the instability. Then we propose two strategies to ensure the load balance among different types of cores. In the end, we simulate this system and use these strategies to demonstrate our design is efficient. It alleviates the instability dramatically and the weighted speedup of heterogeneity-aware static scheduling (HASS) policy we examine outperforms straightforward scheduling (SS) policy by up to 2.4 and heterogeneity-aware dynamic thread migration (HADM) policy exceeds the SS policy by up to 3.