  We study quantum manipulation based on four Majorana bound states in
X-junction geometry. The parameter space of this setup is bigger than of the
previously studied Y-junction and is described by SO(4) symmetry group. In
order for quantum computation to be dephasing free, two Majorana states have to
stay degenerate at all times. We find a condition necessary for that and
compute the Berry's phase, $2\alpha$, accumulated during the manipulation. We
construct simple protocols for the variety of values of $\alpha$, including
$\pi/8$ needed for the purposes of quantum computation. Although the
manipulations in general X-junction geometry are not topologically protected,
they may prove to be a feasible compromise for aims of quantum computation.
