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Federated learning (FL) and split learning (SL) are the two popular distributed machine learning (ML) approaches that provide some data privacy protection mechanisms. In the time-series classification problem, many researchers typically use 1D convolutional neural networks (1DCNNs) based on the SL approach with a single client to reduce the computational overhead at the client-side while still preserving data privacy. Another method, recurrent neural network (RNN), is utilized on sequentially partitioned data where segments of multiple-segment sequential data are distributed across various clients. However, to the best of our knowledge, it is still not much work done in SL with long short-term memory (LSTM) network, even the LSTM network is practically effective in processing time-series data. In this work, we propose a new approach, LSTMSPLIT, that uses SL architecture with an LSTM network to classify time-series data with multiple clients. The differential privacy (DP) is applied to solve the data privacy leakage. The proposed method, LSTMSPLIT, has achieved better or reasonable accuracy compared to the Split-1DCNN method using the electrocardiogram dataset and the human activity recognition dataset. Furthermore, the proposed method, LSTMSPLIT, can also achieve good accuracy after applying differential privacy to preserve the user privacy of the cut layer of the LSTMSPLIT.