In 1985 John Reade determined the spectrum of the Cesâro Operatör which is repre- sented by the matrix: / I 0 0 . . . \ C ı — ı 2 0 ... I regarded as an operatör on the space co of ali null sequences normed by || x j| = sup [ xn [. n> 0 It is the purpose of this paper to determine the spectrum of regarded as an operatör on the 00 space bv of ali sequences x such that lim xn exists and ][ x || = lim | xn 4- 2 ]xn + l-xn | n—>Oo n->00 n=0 < 00 We do so by proving that (C , - XI)-1 GB (bv) for ali XeC such that [ X- | > i •