Let S be a semi-group, and let σ, τ ∈ Antihom(S, S) satisfy τ • τ = σ • σ = id. We show that any solutions f : S → C of the functional equation f(xσ(y)) + f(τ(y)x) = 2 f (x) f (y), x, y ∈ S, has the form f = (m + m • σ • τ)/2, where m is a multiplicative function on S.