The complete theory of a singularity-enhanced finite-difference time-domain (FDTD) method for a sharp diagonal metal edge is presented. This method is very accurate and efficient for modeling printed microwave components with diagonal metal edges including some microstrip patch antennas, various other printed antennas, and printed transmission lines. Considering the singular nature of electromagnetic fields at a sharp metal edge, new FDTD equations are derived for all electric and magnetic nodes near the edge, using a contour-path subcell approach. The new FDTD equations for the affected nodes differ from the standard (Yee's) FDTD equations only by a few additional coefficients, for which complete mathematical expressions are given. Application of this method to several antenna and transmission-line problems demonstrated significantly improved accuracy over previous methods, without any noticeable computing overhead. A coarse grid can be used in conjunction with this method and hence the required computer memory and time can be reduced drastically. We have used the maximum allowed time step in all our applications and the method was always stable.