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Property-oriented concept lattices are systems ofconceptual clusters called property-oriented concepts, which arepartially ordered by the subconcept/superconcept relationships.Property-oriented concept lattices are basic structures used informal concept analysis. In general, a property-oriented con-cept lattice may contain overlapping clusters and is not to be atree construction. Additionally, tree-like classification schemesare appealing and are produced by several clustering methods.In this paper, we present necessary and sufficient conditions oninput data for the output property-oriented concept lattice toform a tree after one removes its greatest element. After ap-plying to input data for which the associated property-orientedconcept lattice is a tree, we present an algorithm for computingproperty-oriented concept lattices.