We demonstrate unique characteristics of the correlated ν = 1 bilayer quantum Hall state in a GaAs/AlGaAs double quantum well. By controlling the total electron density as well as the distribution of electrons in the wells, we measured the magnetoresistance and the Hall resistance especially at around ν = 1. The plateau width of the ν = 1 quantum Hall state is used to estimate the stability of the state and found to be sensitive only to the total electron density, and almost independent of the ratio of electrons between two layers. These experimental data can be interpreted as the existence of incompressible bilayer v = 1 quantum Hall state at any ratio. The impact of the findings on the possibility of observing interlayer quantum coherence, which is theoretically predicted, is also discussed.