Abstract: In open logic the notion of R\|reconstruction plays an essential role. However, R\|reconstructions can be too numerous to compute and to list out. Based on a priority relation a new notion of R\|reconstruction is proposed, which does not have the problem mentioned above. Moreover, the notion is reasonable in characterizing the update of a knowledge base when some priority relation among the pieces of the knowledge base is given. Starting by the model\|theoretic notion of rejection by fact in open logic, the definition of R\|reconstruction is given based on priority relation. Then proved are a series of important properties about this kind of R\|reconstructions, including soundness, existence, monotonicity, and continuity.