In this note we derive a punctured neighborhood theorem for a commuting pair of operators. Throughouth this note suppose $T = (T_1, cdots, T_n)$ be a commuting n-tuple of operators acting on a Hibert space H, let $Lambda[e] = {lambda^k[e], the collection of k - forms}^n_{k=0}$ be the exterior algebra on n generators $e_1,cdots,e_n (e_i wedge e_j = -e_j wedge e_i$ for all i,j = 1,cdots,n$), and write $Lambda(H) = Lambda[e] otimes H$. Let $Lambda(T) : Lambda(H) o Lambda(H)$ be given by $$ (0.1) Lambda(T) (omega otimes x) = sum_{i=1}^{n}{e_i wedge omega) otimes T_ix}. $$