In this paper we propose a new operational semantics, called BCN, which is sound and complete with respect to Clark-Kunen's completion for the unrestricted class of Normal Logic Programs. BCN is based on constructive negation and can be seen as an operational semantics for the class of Normal Constraint Logic Programs (NCLP) over the Herbrand universe. The main features of BCN making it a useful operational mechanism are twofold: First, BCN improves the existing proposals because it is more amenable to a practical implementation. The point is that, instead of computing subsidiary trees, the process of constructing answers for negative goals is reduced to a simple symbolic manipulation plus a constraint satisfaction checking process. Essentially, our approach exploits the definition of negative literals in the completion to interpret the constructive negation meta-rule. Second, the way in which BCN is defined makes it an extensible scheme to NCLP over arbitrary constraint domains.