Multiunit activity (MUA) has been proposed to mitigate the robustness issue faced by single-unit activity (SUA)-based brain-machine interfaces (BMIs). Most MUA-based BMIs still employ a binning method for extracting firing rates and linear decoder for decoding behavioural parameters. The limitations of binning and linear decoder lead to suboptimal performance of MUA-based BMIs. To address this issue, we propose Bayesian adaptive kernel smoother (BAKS) as the feature extraction method and long short-term memory (LSTM)-based deep learning as the decoding algorithm. We evaluated the proposed methods for reconstructing (offline) hand kinematics from intracortical neural data chronically recorded from the motor cortex of a monkey. Experimental results showed that BAKS coupled with LSTM outperformed other combinations of feature extraction method (binning or fixed kernel smoother) and decoding algorithm (Kalman filter or Wiener filter). Overall results demonstrate the effectiveness of BAKS and LSTM for improving the decoding performance of MUA-based BMIs.