In this paper, we report, a terahertz parametric oscillator (TPO), based on degenerate four waves mixing, with the ability to oscillate all four waves participating in the process in a Fabry-Perot cavity using nonlinear third-order nonlinear material of silicon nitride. By adjusting the phase matching conditions  as well as the pump wavelength in a range of 1.055-1.0559, terahertz waves with central frequency in the range of 0.588-2.6826 THz are obtained. The best phase matching conditions occur at central frequency of 1THz, and the peak power of the generated terahertz wave reaches 3.6 μW in a single round trip of the waves within the cavity.