During the last 20 years extreme wildfires have challenged firefighting capabilities. Often, the prediction of the extreme behaviour is essential for the safety of citizens and firefighters. Currently, there are several fire danger indices routinely used by firefighting services, but they are not suited to forecast extreme-wildfire behaviour at the global scale. This article proposes a new fire danger index, the extreme-fire behaviour index (EFBI), based on the analysis of the vertical profiles of the atmosphere above wildfires as an addition to the use of traditional fire danger indices. The EFBI evaluates the ease of interaction between wildfires and the atmosphere that could lead to deep moist convection and erratic and extreme wildfires. Results of this research through the analysis of some of the critical fires in the last years show that the EFBI can potentially be used to provide valuable information to identify convection-driven fires and to enhance fire danger rating schemes worldwide.