A method for replacing cache lines in a computer system having a non-uniform set associative cache memory is disclosed. The method incorporates access latency as an additional factor into the existing ranking guidelines for replacement of a line, the higher the rank of the line the sooner that it is likely to be evicted from the cache. Among a group of highest ranking cache lines in a cache set, the cache line chosen to be replaced is one that provides the lowest latency access to a requesting entity, such as a processor. The distance separating the requesting entity from the memory partition where the cache line is stored most affects access latency.