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 estimating 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 a method which consists of Bayesian adaptive kernel smoother (BAKS) as the firing rate estimation algorithm and deep learning, particularly quasi-recurrent neural network (QRNN), as the decoding algorithm. We evaluated the proposed method for reconstructing (offline) hand kinematics from intracortical neural data chronically recorded from the primary motor cortex of two non-human primates. Extensive empirical results across recording sessions and subjects showed that the proposed method consistently outperforms other combinations of firing rate estimation algorithm and decoding algorithm. Overall results suggest the effectiveness of the proposed method for improving the decoding performance of MUA-based BMIs.