The binary algorithm is a variant of the Euclidean algorithm that performs well in practice. We present a quasi-linear time recursive algorithm that computes the greatest common divisor of two integers by simulating a slightly modified version of the binary algorithm. The structure of the recursive algorithm is very close to the one of the well-known Knuth-Schönhage fast gcd algorithm, but the description and the proof of correctness are significantly simpler in our case. This leads to a simplification of the implementation and to better running times.