Summary: For a general \(n\times n\) real matrix \((a_{ij})\), standard \(O(n^ 3)\) algorithms exist to find its maximum cycle mean, i.e., to find \(\lambda(A)=\max(a_{i_ 1i_ 2}+a_{i_ 2i_ 3}+\cdots+a_{i_ ki_ 1})/k\) over all cyclic permutations \((i_ 1,\dots,i_ k)\) of subsets of the set \(\{1,2,\dots,n\}\). We consider the case when all the elements \(a_{ij}\) take values in a binary set \(\{a,b\}\) and construct an algorithm of complexity \(O(n^ 2)\) which then suffices to find \(\lambda(A)\).