Spiking neural networks are promising for low-energy-consuming computations. Local unsupervised learning methods, such as Spike-Timing-Dependent Plasticity (STDP) are preferable for spiking networks, because are easier to implement in memristive hardware than backpropagation. Existing STDP-based learning methods rely on the sensitivity of STDP to input-output spike correlations. In this work, we propose a novel supervised SNN learning method that leverages such correlations explicitly, thus providing a straightforward way of conveying the feedback signal to the spiking neural network. The method implementation is based on converting an input vector into an array of spike sequences that are correlated with a given output sequence. The practical significance of this approach lies in facilitating the development of compact neural networks that do not rely on global error backpropagation training algorithms. The efficiency of the method is supported by the results of experiments on different benchmark datasets: Fisher’s Iris - 99 \(\,\pm \,\) 1% (using the micro F1-score), Wisconsin Breast Cancer - 95 \(\,\pm \,\) 2%, Scikit-Learn Handwritten Digits - 92 \(\,\pm \,\) 2%. We provide the results obtained with the proposed approach using memristive plasticity models, demonstrating its applicability to real-world memristive devices.