The following functional equation is studied: \[ g(xy) + \mu(y)g(x\psi(y)) = 2g(x)g(y), \text{for all } x, y \in S. \] Here \(S\) is a semigroup, \(\psi:S\to S\) is an anti-endomorphism (which means that \(\psi(xy)=\psi(y)\psi(x)\) for all \(x,y\)), \(\mu:S\to\mathbb{K}\) satisfies \(\mu(x\psi(x))=1\) for all \(x\in S\), \(\mathbb{K}\) is an algebraically closed field of characteristic not equal to \(2\), and \(g:S\to\mathbb{K}\) is the unknown function. The equation generalizes the D’Alembert functional equation to the noncommutative setting. The authors find the general solution of the equation.