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We introduce CoLN, Combined Learning of Neural network weights, a novel method to securely combine Machine Learning models over sensitive data with no sharing of data. With CoLN, local hosts use the same Neural Network architecture and base parameters to train a model using only locally available data. Locally trained models are then submitted to a combining agent, which produces a combined model. The new model's parameters can be sent back to hosts, and can then be used as initial parameters for a new training iteration. CoLN is capable of combining several distributed neural networks of the same kind but is not restricted to any single neural architecture. In this paper we detail the combination algorithm and present experiments with feed-forward, convolutional, and recurrent Neural Network architectures, showing that the CoLN combined model approximates the performance of a hypothetical ideal centralized model, trained using the combination of the local datasets. CoLN can contribute to secure collaborative research, as required in the medical area, where privacy issues preclude data sharing, but where the limitations of local data demand information derived from larger datasets.