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Fisher Linear Discriminant (FLD) is a well-known method for dimensionality reduction and classification that projects high-dimensional data onto a low-dimensional space where the data achieves maximum class separability. To improve the learning performance of FLD algorithm, in this paper we introduce Markov sampling algorithm to generate uniformly ergodic Markov chain samples from a given i.i.d. data of finite size by following the enlightening idea from MCMC methods. Through simulation studies and numerical studies on benchmark repository using FLD algorithm, we found that FLD algorithm based on uniformly ergodic Markov samples generated by the markov sampling algorithm introduced in this paper can provide smaller mean square error compared to the i.i.d. sampling from the same data.