In this research, a new method is discovered (combined method) to accelerate the backpropagation network by using the expected values of source units for updating weights, we mean the expected value of unit by the sum of the output of the unit and its error term multiplied by the factor Beta to accelerate the algorithm and also adjust the value of learning coefficient continuously if the value of energy function E decreases the learning rate is increased by a factor , if the value of the energy function E increases , the value of the learning rate is decreased by a factor . To obtain the optimal weight with minimum iteration and minimum time, we applied a new method on many applications to prove the result of this method (pattern compression, encoding and recognition on Arabic, English digits and alphabetic.