We revisit the conformal anomaly for a Weyl fermion in four dimensions that has generated some debate recently. We employ a perturbative expansion for the metric around Minkowski space, dimensional regularization and a Breitenlohner--Maison prescription for the chiral $\gamma$ matrix. We obtain a vanishing odd-parity contribution for Weyl fermions in four dimensions, while the even-parity contribution is exactly half the one for a Dirac fermion.