Abstract: A language L is the orthogonal concatenation of languages L 1 and L 2 if every word of L can be written in a unique way as a concatenation of a word in L 1 and a word in L 2. The notion can be generalized for arbitrary language operations. We consider decidability properties of language orthogonality and the solvability of language equations involving the orthogonal concatenation operation. We establish a tight bound for the state complexity of orthogonal concatenation of regular languages.