In this study, new models for the merger of two or more inefficient units are presented. The discussed mergers in this study are horizontal and acquisition mergers. In presented models, unlike the previously presented models, the mergers are done non-radially; indeed, managers can manage each of the indicators separately in the presented new merger process. In this regard, the efficient frontier of the production possibilities set does not change, and the merger of several units does not affect the efficiency score of other decision-making units. Also, by merging via the new models one can obtain a strong efficient unit with the most productive scale size. The presented models are applied to the horizontal and acquisition merger of Iranian banks.