A new type of biepitaxial grain-boundary junction with a lattice misorientation at the boundary of 20 degrees, was fabricated utilizing an obliquely cut SrTiO3 (STO) substrate. The structure of the junction which was the grain boundary between the two domains made of Y1Ba2Cu3O7-delta (YBCO) layer and YBCO/CeO2/YSZ (yttria-stabilized zirconia) multilayer was a b-axis tilt or a b-axis twist grain boundary. These were confirmed by X-ray diffraction (XRD) measurements. The former showed RSJ type I-V characteristics and SQUID oscillations. Its I(c)R(n) was 1.6 mV at 20 K. The latter did not show any weak-link behavior.