The two-dimensional elastic wave propagation in an isotropic bent plate with a curved corner is analyzed theoretically to investigate the reflection and transmission characteristics of Lamb waves at the corner section. The modal amplitudes of reflected and transmitted Lamb waves, when a monochromatic single Lamb wave mode impinges on the corner section, are calculated by the modal decomposition method with the impedance matrices. Furthermore, the reciprocity relation between the incident and reflected/transmitted Lamb wave modes is derived. The reflection and transmission of the lowest-order symmetric and antisymmetric modes below the cut-off frequencies of higher-order modes are found to be markedly influenced by the frequency, bend angle, and bend radius. In particular, the reflection and transmission coefficients are shown to have local minima and maxima on the frequency axis due to the multiple reflections at the boundaries between flat and corner regions.