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YBa2Cu3O7-y with high grain alignment has been successfully fabricated by a modified powder melting process at a temperature of ~930oC which is near the eutectic point of the starting materials Y2BaCuO5, BaCuO2, and CuO. In terms of the levitation force and YBa2Cu3O7-y grain alignment, the best result was shown in a sample having a Y2BaCuO5:BaCuO2:CuO molecular ratio of 1:3:5. In the present work, the Cu-surplus eutectic liquid was completely absorbed by use of a Y2BaCuO5 substrate, by which the final composition was driven to stoichiometric YBa2Cu3O7-y. The results were comparable to those obtained by the conventional melt-texture-growth process. A new invariant point apparently occurred at ~930-940oC owing to an interfacial reaction between YBa2Cu3O7-y matrix and Y2BaCuO5 substrate.