The latest Sloan Digital Sky Survey data reveal a prominent bifurcation in the distribution of debris of the Sagittarius dwarf spheroidal (Sgr) beginning at a right ascension of α ≈ 190°. Two branches of the stream (A and B) persist at roughly the same heliocentric distance over at least 50° of arc. There is also evidence for a more distant structure (C) well behind the A branch. This paper provides the first explanation for the bifurcation. It is caused by the projection of the young leading (A) and old trailing (B) tidal arms of the Sgr, while the old leading arm (C) lies well behind A. This explanation is only possible if the halo is close to spherical, as the angular difference between the branches is a measure of the precession of the orbital plane.