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The study presents a new classification algorithm and a new online training mode used for learning the parameters of a Bayesian RBFNN (radial basis function neural network) equaliser in a non-linear time-varying channel. The classification algorithm is used to determine the centres of the hidden layer neurons that are equal to the channel states. This proposed unsupervised classification algorithm is based on both the K-means and the rival penalised competitive algorithms. Its main advantage is neither an initialisation phase nor a knowledge of the channel states number is required. The connections of weights and the spread of the hidden neurons are learned by the gradient descent algorithm, which applies a new proposed training mode. This training mode combines the advantages of both the online and the offline training modes such as stability and good speed of convergence. The performances of the RBFNN equaliser trained by the proposed method are shown in comparison with the performances of the optimal Bayesian equaliser and those of the same equaliser trained by other known training modes. All these performances are studied by using different types of channels.