We present proofs of the stability and convergence of Self-organizing feature map (SOFM) neural network with time-invarient learning rate and binary reinforcement function. One of the major problems in Self-organizing feature map neural network concerns with learning rate-"Kalman Filter" gain in stochsatic control field which is monotone decreasing function and converges to 0 for satisfying minimum variance property. In this paper, we show that the stability and convergence of Self-organizing feature map neural network with time-invariant learning rate. The analysis of the proposed algorithm shows that the stability and convergence is guranteed with exponentially stable and weak convergence properties as well.s as well.