This paper is on the Consensus problem, in the context of asynchronous distributed systems made of n processes, at most f of them may crash. A family of failure detector classes satisfying a Perpetual Accuracy property is first defined. This family includes the failure detector class S (the class of Strong failure detectors defined by Chandra and Toueg) central to the definition of a class (Sx) where x is the minimum number (x 1) of correct processes that can never be suspected to have crashed. Then, a protocol that solves the Consensus problem is given. This protocol works with any failure detector class (Sx) of this family. It is particularly simple and uses a Reliable Broadcast protocol as a skeleton. It requires n,x+ 1 communication steps, and its communication bit complexity is n , x + 1n , 1jvj (where jvj is the maximal size of an initial value a process can propose).