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A fabrication technique for a single-domain Y123 crystal by top-seeded melt processing was developed using two step undercooling. At the first undercooling step, the Y123 nucleus was stabilized, and increased growth rate was intended at the second undercooling step. By the two step undercooling method, the processing time required for the growth of Y123 single-domain crystal was significantly reduced without degradation of the superconducting properties. The microstructures and textures of Y123 samples prepared by two step undercooling were also investigated.