As a result of studying the selection procedures (request for valuation, request for proposals, auction, tender) of private companies for creating public-private partnerships, some shortcomings of their work were identified. Firstly, only one company becomes a winner as a result of the selection, and the other applicants are excluded from participation in the partnership. Secondly, only financial characteristics of the companies that are potential participants are analyzed, some important factors of the legal and professional nature are not considered. The purpose of the article is to offer a procedure for preliminary and main selection (improve the existing procedure). It should be noted that we examine the development projects of social infrastructure, so the selection of companies is specific for the field assets: land, buildings, money. The pre-selection procedure is based on the analysis of legal and professional factors. The main selection procedure is based on the quantitative data of the assets of the company and forms partnerships of the companies whose assets are complementary to each other (the arguments of such sets of assets of the companies are listed in the first part of the work). In contrast with the existing selection procedure, the public-private partnership with the participation of several private companies can be identified as a result of improved selection procedure. This procedure can also create several public-private partnerships. The construction procedure of public-private partnerships is described using graph theory – coloring of vertices and edges of a graph according to certain rules. At the end of the article, there is a remark that the proposed procedure produces a result that is no less and in some cases even more effective than the current ones.