  On a star graph made of $N \geq 3$ halflines (edges) we consider a
Schr\"odinger equation with a subcritical power-type nonlinearity and an
attractive delta interaction located at the vertex. From previous works it is
known that there exists a family of standing waves, symmetric with respect to
the exchange of edges, that can be parametrized by the mass (or $L^2$-norm) of
its elements. Furthermore, if the mass is small enough, then the corresponding
symmetric standing wave is a ground state and, consequently, it is orbitally
stable. On the other hand, if the mass is above a threshold value, then the
system has no ground state. Here we prove that orbital stability holds for
every value of the mass, even if the corresponding symmetric standing wave is
not a ground state, since it is anyway a {\em local} minimizer of the energy
among functions with the same mass. The proof is based on a new technique that
allows to restrict the analysis to functions made of pieces of soliton,
reducing the problem to a finite-dimensional one. In such a way, we do not need
to use direct methods of Calculus of Variations, nor linearization procedures.
