We present a systematic study of a close-ring pair based freestanding metamaterial fabricated by double-layer, self-aligned photolithography. Terahertz time-domain spectroscopy transmission measurements and numerical simulations have revealed negative index of refraction in the frequency range of 0.66-0.90 THz under normal wave incidence. The observed resonance behaviors can be well explained by a theoretical circuit model. The electromagnetic properties and the figure of merit of such close-ring metamaterials are also explored in terms of geometrical parameters of the unit cell with a goal of providing optimized design for three-dimensional metamaterials and potential device applications.