We present unconditionally stable Non-orthogonal Locally One Dimensional (LOD) finite-difference time-domain (FDTD) method. The non-orthogonal formulation can be useful to extend the LOD-FDTD methods for curved discontinuities so as to obtain more accurate results with reduced computational resources. Formulations for CPML as well as scattered-field formulation are provided. Numerical simulations are used to demonstrate the accuracy and improvement of the proposed method over the conventional and non-orthogonal FDTD algorithms.