  In this note, we show that sub-Riemannian manifolds can contain branching
normal minimizing geodesics. This phenomenon occurs if and only if a normal
geodesic has a discontinuity in its rank at a non-zero time, which in
particular for a strictly normal geodesic means that it contains a non-trivial
abnormal subsegment. The simplest example is obtained by gluing the
three-dimensional Martinet flat structure with the Heisenberg group in a
suitable way. We then use this example to construct more general types of
branching.
