  We consider the braiding of Kramers pairs of Majorana bound states. We derive
the most general transformation on the many-body ground state that is applied
as the result of such a braiding process. The result is derived in the context
of a simple toy model, but we will show that it has the most general form that
is compatible with local and global conservation of electron parity. In
accordance with earlier work the resulting transformation turns out to be path
dependent, which shows that Kramers pairs of Majorana bound states cannot be
used for topological quantum computation. We also discuss under which
conditions the result is path independent and corresponds to two independent
exchanges of pairs of Majorana bound states.
