The resistive transitions R(T) and the current-voltage (I-V) in fields up to 5 T were measured in a melt-textured YBa2Cu7-delta (YBCO) sample consisting of two single-grain domains separated by an inter-domain border, and in a single-grain sample cut from the same pellet and oxygenated in such conditions that ensure the optimum oxygenation of the grains. From comparing the two sets of results, we were able to suggest that the inter-domain border consists of oxygen-deficient YBCO with thickness smaller than 6 mum, having a slightly lower critical temperature, a higher anisotropy factor and without strong pinning centers. From applications point of view, our work shows that, for improving the superconducting properties of large multiple-domain melt-textured pellets. an oxygenation process much longer than that required for optimum grain properties is needed. (C) 2001 Published by Elsevier Science B.V.