It is an old problem posed by Bennett and Lutzer whether every perfect GO-space has a perfect orderable extension. As an approach to this problem, we prove that, for a perfect GO-space X, X has a perfect linearly ordered extension if and only if there is a o-discrete subset F such that GOx (ф, X-F, F, ф) is perfect, where GOx (ф, X-F, F, ф) is the ordered set X with the topology defined so that every point in F is isolated and every point in X-F has the usual interval neighborhood base.