  It is well known that one-dimensional Klein-Gordon lattices with
nearest-neighbor interactions can support multibreathers with phase differences
between the successive "central" oscillators $\phi_i=0\ \mbox{or}\ \pi$
(standard configurations). In this paper we prove that in this kind of systems,
the standard configurations are the only possible ones, so phase-shift
breathers (configurations with $\phi_i\neq0,\, \pi$) cannot be supported. This
fact also determines the linear stability of the existing multibreathers.
