In this paper, an optimization of the non-binary polar decoders is realized in two aspects. Firstly, the L-bubble sorter, a simplified version of the Extended Min-Sum (EMS) algorithm, is applied to the non-binary polar decoder. Then, a criterion is set to evaluate the relative reliability of the two inputs of the non-binary kernel. Accordingly, the kernel processes the two inputs differently. The proposed asymmetrical process reduces the decoder's complexity by reducing the number of candidates to be computed. Over the Galois field of size 64, the size of computed candidates is reduced by a factor of 2 compared to the EMS algorithm. When simulated over a real additive white Gaussian noise channel with a binary phase shift keying modulation, the proposed decoder showed a performance degradation of 0.25 dB compared to the min-sum algorithm. However, when the cyclic-code shift keying modulation is used, the degradation is reduced to around 0.1 dB.