The majority of extreme preterm infants require endotracheal intubation and mechanical ventilation (ETT-MV) during the first days of life to survive. Unfortunately this therapy is associated with adverse clinical outcomes and consequently, it is desirable to remove ETT-MV as quickly as possible. However, about 25% of extubated infants will fail and require re-intubation which is also associated with a 5-fold increase in mortality and a longer stay in the intensive care unit. Therefore, the ultimate goal is to determine the optimal time for extubation that will minimize the duration of MV and maximize the chances of success. This paper presents a new objective predictor to assist clinicians in making this decision. The predictor uses a modern machine learning method (Support Vector Machines) to determine the combination of measures of cardiorespiratory variability, computed automatically, that best predicts extubation readiness. Our results demonstrate that this predictor accurately classified infants who would fail extubation.