Previous papers have determined the corner correction for axial current in a conducting wedge with an internal right angle. The corner constant for transverse current is now defined to correct the power dissipation of the simple impedance solution at the corner. Previous results are used to calculate its value for the case of an internal right angle in this paper. For arbitrary internal angles an integral representation is found for the transverse corner constant; it is used to obtain the transverse corner constant in the case of an external right angle. Furthermore, it is also briefly shown how the corner corrections for both axial and transverse current apply to the calculation of the propagation constant in a waveguide.