Based on the simple framework of the recharge oscillator for El Niño-Southern Oscillation (ENSO), this paper describes the formulation of a coupled stability index for the large-scale tropical ocean-atmosphere interactions in the equatorial Pacific region. This index, referred to as the Bjerknes (BJ) stability index, takes its negative contributions from the mean upwelling and thermal damping and its positive contributions from the thermocline, the zonal advection, and the Ekman feedbacks. The validity of the BJ stability index formula is tested through a detailed eigen-analysis of an intermediate-coupled model, which shows that the BJ stability index captures the dependence of growth rate of the leading coupled ENSO-like mode on various climate conditions. The general formula of the BJ stability index may be useful for assessing the coupled stability of ENSO and its sensitivity to changes in tropical climate conditions.