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This work deals with data-driven control for non-minimum phase (NMP) systems, where the goal is to design a controller for a plant whose model is unknown by using a batch of input-output data collected from it. The approach is based on the Model Reference paradigm, where a transfer function matrix - the reference model - is used to specify the desired closed-loop performance. The NMP systems issue in Model Reference approaches is a well-known problem in control literature and it is no different in data-driven methods. This work explains how to adapt the formulation of the Optimal Controller Identification (OCI) method to cope with this class of systems. Considering a convenient parametrization of the reference model and a flexible performance criterion, it is possible to identify the NMP transmission zeros of the plant along with the optimal controller parameters, as it will be shown. Both diagonal and block-triangular reference model structures are treated in detail. Simulation examples show the effectiveness of the proposed approach., Competing Interests: Declaration of competing interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper., (Copyright © 2024 International Society of Automation. Published by Elsevier Ltd. All rights reserved.)