Replacement policies play a major role in determining the overall performance expected from the cache memories while minimizing the large latency gap between the processor and the main memory. Existing techniques, including the well-known Least Recently Used (LRU) policy aim at evicting the blocks that have lesser temporal locality during block replacement. The rational behind the eviction of low temporal block is to increase temporal locality of the resident blocks in the cache which increases the cache hit rate. However, such technique often overlooks the factor associated with the frequent eviction, followed by re-accessing of some blocks that lead to the phenomenon of thrashing, particularly in the Last Level Caches. In this paper, we have proposed a new cache replacement policy called RECminThrash for the last level cache that takes both temporal locality and thrashing factors into account in order to improve cache performance. In particular, our proposed policy RECminThrash compares the eviction counts of a few less recently accessed blocks and selects the one that has the lowest eviction count to reduce thrashing in the cache. At the same time, it maintains high temporal locality in the resident blocks as the victim is chosen from one of the less re-used blocks in the cache. Experimental results reveal that RECminThrash shows 7.5% reduction in overall eviction count, 14% improvement in hit rate, and 7% improvement in performance over the traditional LRU technique.