  We study full exact functors between triangulated categories. With some
hypotheses on the source category we prove that it admits an orthogonal
decomposition into two pieces such that the functor restricted to one of them
is zero while the restriction to the other is faithful. In particular, if the
source category is either the category of perfect complexes or the bounded
derived category of coherent sheaves on a noetherian scheme supported on a
closed connected subscheme, then any non-trivial exact full functor is faithful
as well. Finally we show that removing the noetherian hypothesis this result is
not true.
