Let B be a p-block of cyclic defect of a Hecke order over the complete ring
Z[q]([q-1,p]); i.e, module [q - 1] it is a p-block B of cyclic defect of t
he underlying Coxeter group G. Then B is a tree order over Z[q]([q-1,p]) to
the Brauer tree of B. Moreover, in case 1 is the principal block of the He
cke order of the symmetric group S(p) on p elements, then B can be describe
d explicitly. In this case a complete set of nonisomorphic indecomposable C
ohen-Macaulay B-modules is given.