Summary: A new approach is used to obtain the transient probabilities of the \(M/M/1\) queueing system. The first step of this approach deals with the generating function of the transient probabilities of the uniformized Markov chain associated with this queue. The second step consists of the inversion of this generating function. A new analytical expression of the transient probabilities of the \(M/M/1\) queue is then obtained.