Tractable classes constitute an important issue in Artificial Intelligence to define new islands of tractability for reasoning or problem solving. In the area of constraint networks, numerous tractable classes have been defined, and recently, the Broken Triangle Property (BTP) has been shown as one of the most important of them, this class including several classes previously defined. In this paper, we propose a new class called ETP for Extendable-Triple Property, which generalizes BTP, by including it. Combined with the verification of the Strong-Path-Consistency, ETP is shown to be a new tractable class. Moreover, this class inherits some desirable properties of BTP including the fact that the instances of this class can be solved thanks to usual algorithms (such as MAC or RFL) used in most solvers. We give the theoretical material about this new class and we present an experimental study which shows that from a practical viewpoint, it seems more usable in practice than BTP.