We have fabricated high-$ extrm{T}_c$ superconducting $ extrm{YBa}_{2} extrm{Cu}_{3} extrm{O}_{7-x}$(YBCO) grain boundary junctions at a step-edge on (001) $ extrm{SrTiO}_3$(STO) substrates. A diamond-like carbon (DLC) film grown by plasma enhanced chemical vapor deposition were used as an ion milling mask to make steps on the STO (100) single crystal and was removed by an oxygen reactive ion etch process. The c-axis oriented YBCO and TO thin films were deposited epitaxially on the STO substrate with a step-edge by pulsed laser deposition. The grain boundary junctions were formed at the top and the bottom of the step. The junctions worked at temperatures above 77 K, and had IulcornerRulcorner products of 7.5mV at 16K and 0.3 mV at 77K, respectively. The I-V characteristics of these junctions showed the shape of the two noisy resistively shunted junction model.