A new frame discretization method for treating non-matching discrete interfaces is presented based on the method of localized Lagrange multipliers, which introduces the frame domain lying between the two interfacing parts. The required interface compatibility conditions are then enforced independently between the master domain interface nodes and the frame nodes, and the slave domain interface nodes and the same frame nodes. The frame nodes are determined so as to satisfy the mean coordinates, including the frame node to be determined, of the nearest interface element of the master domain for each of the slave domain interface nodes. The roles of the two domains may interchange, resulting in a unique determination of the frame elements for each case. The interface compatibility conditions thus obtained satisfy energy conservation, especially when the interface gaps are unavoidable while requiring no special treatments for the boundary nodes that are often required in mortar and allied methods. Consequently, the proposed method can effectively deal with the non-matching interface regardless of the geometric complexity and element type. Numerical examples illustrate the simplicity of the proposed method and offer improved accuracy for interfaces with gaps and as good of an accuracy as other methods when there are no gaps, while preserving implementation simplicity. (C) 2019 Elsevier B.V. All rights reserved.