boundary. Recently, this result was improved in [15] to show second-order convergence of solutions including Thom's vorticity condition for solving the incompressible Navier-Stokes equations is generally known as a first-order method since boundary vorticity for the steady Stokes equations using the local truncation error for the value of boundary vorticity is first-Thom's boundary condition. In the present paper, a disorder accurate. In the present paper, it is shown that convergence crete error for boundary voriticity is estimated to be of in the boundary vorticity is actually second order for steady proborder h 2 for steady state Navier-Stokes equations and for lems and for time-dependent problems when t Ͼ 0. The result is time dependent problems for t Ͼ 0. The uniform secondproved by looking carefully at error expansions for the discretization order convergence of the vorticity values here and in [15] which have been previously used to show second-order convergence of interior vorticity. Numerical convergence studies confirm is established by more carefully examining the asymptotic the results. At t ϭ 0 the computed boundary vorticity is first-order error results from [11]. The fundamental idea here is very accurate as predicted by the local truncation error. Using simple simple: that Thom's voriticity boundary condition is genermodel problems for insight we predict that the size of the secondated from a second-order approximation of the more funorder error term in the boundary condition blows up like C/͙t as damental no-slip condition. We prove that Thom's boundt Ǟ 0. This is confirmed by careful numerical experiments. A similar phenomenon is observed for boundary vorticity computed ary approximation is a second-order method even at the using a primitive method based on the staggered marker-and-cell boundary, contrary to popular belief. We demonstrate this grid.