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Akbari and Alipour defined $l(n)$ as the least integer such that every properly edge-colored $K_{n,n}$, which contains at least $l(n)$ different colors, admits a multicolored perfect matching. They conjectured that $l(n)\\leq n^2/2$ if $n$ is large enough. In this note we prove that $l(n)$ is bounded from above by $0.75n^2$ if $n>1$. 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