  In this note, we construct a 2-basic set of the alternating group \A_n. To do
this, we construct a 2-basic set of the symmetric group \sym_n with an
additional property, such that its restriction to \A_n is a 2-basic set. We
adapt here a method developed in \cite{BrGr} for the case when the
characteristic is odd. One of the main tools is the generalized perfect
isometries defined by K\"ulshammer, Olsson and Robinson in \cite{KOR}.
