The Distributed Consensus problem assumes that all processors in the system have some initial values; the goal is to make all non-faulty processors agree on one of these values. This paper investigates the time needed to reach consensus in a partially synchronous model with omission failures. In this model, the processors have no direct knowledge about time, but the time between consecutive steps of each processor is always between two known constants c1 and c2; the ratio C = c2/c1 measures the timing uncertainty in the system. Moreover, messages are delivered within time d. This paper provides an improved protocol for the above problem. When the majority of the processors is fault-free, the protocol achieves consensus in time 3(qq+1)d+Cd, where φ is the actual number of faults in a specific execution of the protocol. This will allow an increase in efficiency up to 25% over the existing protocol which requires time 4(qq+1)d+Cd.