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A subcell model for thin wires in the finite-difference time-domain method using modified telegraphers equations has been developed by Holland et al. (1981). In this paper, we present an extension of their algorithm, which allows arbitrarily located and oriented wires with respect to the Cartesian grid. This is important to be able to accurately model wires that cannot be aligned to the Cartesian grid, e.g., tilted wires and circular loop wires. A symmetric coupling between field and wires yields a stable time-continuous field-wire system and the fully discrete field-wire system is stable under a Courant-Friedrich-Lewy (CFL) condition. The accuracy and excellent consistency of the proposed method are demonstrated for dipole and loop antennas with comparisons with the method of moments and experimental data.