Heat integration by a heat exchanger network (HEN) is an important topic in chemical process system synthesis. From the perspective of optimization, the simultaneous synthesis of HEN belongs to a mixed-integer and nonlinear programming problem. Both the stage-wise superstructure (SWS) model and the chessboard model are the most widely adopted and belong to structural models, in which a framework is assumed for stream matching, and the global optimal solution outside its feasible domain may be defined by the framework. A node-wise non-structural model (NW-NSM) is proposed to find more universal stream matching options, but it requires a mass of structural variables and extra multiple correction strategies. The aim of this paper is to develop a novel matrix non-structural model (M-NSM) for HEN without stream splits from the perspectives of global optimization methods and superstructure models. In the proposed M-NSM, the heat exchanger position order is quantized by matrix elements at each stream, and a HEN structure is initialized by the random generation of matrix elements. An approach for solving HEN problems based on a matrix real-coded genetic algorithm is employed in this model. The results show that M-NSM provides more flexibility to expand the search region for feasible solutions with higher efficiency than previous models.