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A new cavity that is composed of left-handed material (LHM) has been proposed. The cavity has size-independent resonant frequency and very high quality factor. In a 2D closed square cavity, the first and third quadrants are filled with LHM and the other two quadrants are filled with right-handed material (RHM). Both LHM and RHM are realized using the LC-loaded transmission line networks. Simulations have been conducted using Agilent's advanced design system (ADS) to investigate the physical properties of the cavity. Analytical and simulation results prove that the new cavity's resonant frequency is independent of the size of cavity. When the surface resistance of the enclosure is considered, the new cavity has a much higher quality factor compared to a conventional cavity.