An exact analytical dispersion relation is derived for transverse-magnetic modes with kz=0 in a particular two-dimensional rectangular photonic band gap structure. The dispersion relation is analyzed, and the dispersion characteristics are determined. Analytical results are compared with results from the Massachusetts Institute of Technology Photonic Band Gap Structure Simulator (PBGSS) code. The error tolerance in the PBGSS code is established. Finally, the attenuations of modes with frequencies in global band gaps are computed analytically.