In this Note, we give a new method to compute the Hilbert basis of the semigroup of certain positive divisors supported on the exceptional divisor of a normal surface singularity. Our approach is purely combinatorial and enables us to avoid the long calculation of the invariants of the ring as it is presented in the work of Altinok and Tosun. (C) 2010 Academie des sciences. Published by Elsevier Masson SAS. All rights reserved.