  For most optimisation methods an essential assumption is the vector space
structure of the feasible set. This condition is not fulfilled if we consider
optimisation problems over the sphere. We present an algorithm for solving a
special global problem over the sphere, namely the determination of Fr\'echet
means, which are points minimising the mean distance to a given set of points.
The Branch and Bound method derived needs no further assumptions on the input
data, but is able to cope with this objective function which is neither convex
nor differentiable. The algorithm's performance is tested on simulated and real
data.
