A new scheme of static surface plasmon polaritons(SPPs) interferometer of the terahertz (THz) range is described. The interference pattern is formed due to interaction of two converging SPP beams that have run different distances. The original SPP beam is splitted and reflected by a flat beam splitter and a mirror disposed of the waveguiding surface and normally to it. By varying the distance spacing the splitter and the coupling element one can change the pattern period. Execution of the pattern enables one to determine both the real and imaginary part of the SPPs refractive index, which is uniquely related to the dielectric constant of the surface and the optical characteristics of its transition layer. The operating time of the interferometer is determined by the photodetector time constant, which is extremely important for studying fast processes on a conducting surface. The interferometer can work with broadband THz radiation sources (such as synchrotrons or pulsed lasers) as well.