Summary: Intersections of perfect 1-error correcting binary codes are studied. It is proved that for any two integers \(k_1\) and \(k_2\) satisfying \(1\leq k_i \leq 2^{(n+1)/2-\log(n+1)}\), \(i=1,2\) there exist perfect codes \(C_1\) and \(C_2\), both of length \(n=2^m-1\), \(m\geq 4\), with \(|C_1\cap C_2|= 2k_1k_2\).