In numerical solutions of fluid flow, vorticity can be generated by truncation errors. We analyze this phenomenon for linearized equations and give conditions for preventing it. The Lax--Wendroff method that meets these constraints is essentially unique, although there are two distinct interpretations, and also turns out to have optimal properties regarding stability and truncation error. The extension of the scheme to unstructured grids is given, together with some discussion of practical problems to which these schemes might bring improvement.