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For µ given latin squares of order n, they have k intersection when they have k identical cells and n 2 − k cells with mutually different entries. For each n ≥ 1 the set of integers k such that there exist µ latin squares of order n with k intersection is denoted by I µ [n]. In a paper by P. , I 3 [n] is determined completely. In this paper we completely determine I 4 [n] for n ≥ 16. For n ≤ 16, we find out most of the elements of I 4 [n].