In this paper we present our own real time speaker-independent continuous phone recognition (Spirit) using Context-Independent Continuous Density HMMs (CI-CDHMMs) modeled by Gaussian Mixtures Models (GMMs). All the parameters of our system are estimated directly from data by using an improved Viterbi alignment process instead of the classical Baum-Welch estimation procedure. Generally, in the literature the Viterbi training algorithm is used as a pretreatment to initialize HMMs models that will be most often re-estimated by using complex re-estimation formula. In order to evaluate and compare the performance of our system with other previous works, we use the TIMIT database. The duration test of our recognition system for each sentence is between 2 seconds (for short sentences) to 12 seconds (for long sentences). We get, by combining the 64 possible phones into 39 phonetic classes, a phone recognition correct rate of 71.06% and an accuracy rate of 65.25%. These results compare favorably with previously published works.