This paper proposes an alternative learning algorithm for a stereophonic acoustic echo canceller without pre-processing which can identify the correct echo-paths. By dividing the filter coefficients into the former/latter parts and updating them alternatively, conditions both for unique solution and for perfect echo cancellation are satisfied. The learning for each part is switched from one part to the other when that part converges. Convergence analysis clarifies the condition for correct echo-path identification. For fast and stable convergence, a convergence detection and an adaptive step-size are introduced. The modification amount of the filter coefficients determines the convergence state and the step-size. Computer simulations show 10 dB smaller filter coefficient error than those of the conventional algorithms without pre-processing.