Blind adaptive systems based on the Euclidean distance (ED) between the distribution function of the output samples and that of a set of random symbols generated at the receiver matching with the distribution function of the transmitted symbol points estimate the ED at each iteration time to examine its convergence state or its minimum ED value. The problem is that this ED estimation obtained by block?data processing requires a heavy calculation burden. In this paper, a recursive ED estimation method is proposed that reduces the computational complexity by way of utilizing the relationship between the current and previous states of the datablock. The relationship provides a ground that the currently estimated ED value can be used for the estimation of the next ED without the need for processing the whole new data block. From the simulation results the proposed recursive ED estimation shows the same estimation values as that of the conventional method, and in the aspect of computational burden, the proposed method requires only O(N) at each iteration time while the conventional block?processing method does $O(N^2)$.