Multi-frequency, polarimetric VLA observations of the non-thermal filaments (NTF's), G0.08+0.15, and G359.96+0.09, also known as the Northern and Southern Threads are presented at 20, 6, 3.6 and 2 cm, with high enough spatial resolution to be resolved for the first time at 6 and 3.6 cm. The 20 cm image reveals a wealth of new detail in the radio sources lying within the inner 60 pc of the Galaxy. The Southern Thread has a prominent split along its length, similar to splitting at the ends of previously studied NTF's. With resolutions as fine as 2'', the 3.6 and 6 cm images reveal a high degree of continuity and little substructure internal to the filament. The spectral index of the Northern Thread has been determined over a broad range of frequencies. Its flux density falls with frequency, alpha=-0.5 between 90 and 6 cm, and becomes much steeper (alpha=-2.0) between 6 and 2 cm. The spectral index does not vary significantly along the length of the Northern Thread, which implies either that the diffusion timescale for the emitting electrons is less than their synchrotron lifetime, or that the emitting electrons are reaccelerated continuously at multiple positions along the filament. Because of the lack of spectral index variation, we have not located the source of relativistic electrons. Polarization observations at 6 and 3.6 cm confirm the non-thermal nature of the emission from the Northern Thread. The fractional polarization in the Northern Thread reaches 70 rotation measures ( RM > 2000 rad/m2) have been observed with irregular variations across the filament.The intrinsic magnetic field in the Northern Thread is predominantly aligned along its long axis.