Abstract: We compute the spectrum of the Schreier graph of the symmetric group S_n corresponding to the Young subgroup S_2 x S_{n-2} and the generating set consisting of initial reversals. In particular, we show that this spectrum is integral and for n > 8 consists precisely of the integers {0, 1, . . . , n}. This implies that these graphs form a family of expanders (with unbounded degree).