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This work presents an extension of the recently developed finite-difference time-domain (FDTD) technique for modeling electromagnetic wave interactions with bianisotropic (BI) media, known as BI-FDTD, to include the more general class of bianisotropic materials. This new FDTD formulation is called BA-FDTD. The theoretical foundation for this method is based on a wavefield decomposition technique. The formulations based on the application of this wavefield decomposition technique to BA media will be presented. Validations of this new model are demonstrated for the interaction of an electromagnetic wave propagating transversely through a uniaxial BA half-space.