In this note, we construct a 2-basic set of the alternating group An. To do this, we construct a 2-basic set of the symmetric group Sn with an additional property, such that its restriction to An is a 2-basic set. We adapt here a method developed by Brunat and Gramain (J. Reine Angew. Math., to appear) for the case when the characteristic is odd. One of the main tools is the generalized perfect isometries defined by Külshammer et al. (Invent. Math. 151, 513–552, (2003)).