Radial Basis Function networks (RBF) is one form of feed forward neural network architecture which is popular besides Multi Layer Preceptor (MLP). It is widely used especially in identifying a black box system. In many cases, identifying of the system process normally has lack of data or may lose some packets data needed in the identifying process. Finite Difference approach with its enhancement, Richardson Extrapolation, is used to improve the learning performance especially in the non linear learning parameter update for identifying system with lost packet data case in online manner. Since initializing of non linear learning's parameters is crucial in RBF networks' learning, random initialization is placed with some clustering method. Some unsupervised learning methods such as, K means clustering and Fuzzy K means clustering are used to replace it. All the possible combination methods in the initialization and update process try to improve the whole performance of the learning process regarding to the system identification with lost packet data case. It can be showed that Finite difference approach with dynamic step size on Recursive Prediction Error for the non linear parameter update with appropriate initialization method succeed to perform better performance compared to Extreme Learning Machine (ELM) as the previous learning method. © 2009 IEEE.