Supersonic transverse jet flow-field has an important role for supersonic combustor in scramjet engines. Supersonic speed induces the difficulty in unsteady measurements, because characteristics time is very short in the flow. Lacks of time-series data make the combustor difficult to develop. To investigate the jet unsteady motion, high-speed framing camera captured 100 successive schlieren images of the supersonic transverse jet flow-field with 250 kHz sampling rate. The mainstream Mach number was 2.0 and the injectant was helium gas, simulating fuel hydrogen. This work revealed the effects of density-weighted jetto-crossflow velocity ratio (blowing ratio: r) and the injector diameter (D) on the motion of the jet boundary. Newly suggested image processing, based on the Sobel spatial filter, efficiently tracked the jet boundary from the time-series schlieren images. 2700 sample data gave the probability density function (PDF) of the jet boundary. The PDF distributions indicated the jet penetration was insensitive to both r and D in rD space. The jet spreading, however, was sensitive to both r and D even in rD space. This was due the compressibility effect generated at the near field of injector. Remapping the time-series jet boundary as the time-space jet trajectory indicated the convective velocity of the large eddies in the jet was insensitive to r and D. It was constant of 460 m/s. The map gave us another important information on the jet motion: cycle of high-penetrated eddy formation in the jet. Spectrum analysis of the time-space jet trajectory investigated the shedding frequencies of highpenetrated eddy in the transverse jet. As the results, we find out that the high-penetrated eddy occurred at comparatively various frequencies. The specific amplified frequency of the jet instability probably did not exist at the far field of supersonic transverse injection.