We have developed a phenomenological model, based on the \Iavailable\i and accepted information for the Centauro events. Our model attempts to explain the observed features of the average event and to estimate characteristic thermodynamic quantities, such as ε, μ, Τ, whose knowledge is necessary for an educated suggestion of a possible phase transition to quark matter in a highly dense nuclear system. The model we presented makes certain plausible assumptions and arguments, which do not conflict with any known theory nor contradict any existing experimental data. The important assumptions are: the collision of a medium-14 mass cosmic ray nucleus with an Ν nucleus and the small changes cf the fireball entropy, volume and temperature during the phase transition. The justification of these assumptions is given by the self- consistency of the model and the estimated auantities and the reasonable and plausible values of these quantities, which are also within the range considered to be necessary for the phase transition. Our "Centauro" model is (to our knowledge) the only one capable of being tested at RHIC and the LHC. In view of the highly interesting and still puzzling Centauro events, we believe that every effort should be made to implement appropriate measurements of particle multiplicity, ID, energy content and <p > Τ in the fragmentation rapidity region. It may give a direct and undoubted indication of quark matter formation in a highly dense nuclear system and solve the mystery of the Centauro and other exotic cosmic ray events. At the same time, the possibility of observing "strangelets" adds a new dimension of excitement to these measurements.