  We establish an existence and uniqueness result for a class of
multidimensional quadratic backward stochastic differential equations (BSDE).
This class is characterized by constraints on some uniform a priori estimate on
solutions of a sequence of approximated BSDEs. We also present effective
examples of applications. Our approach relies on the strategy developed by
Briand and Elie in [Stochastic Process. Appl. 123 2921--2939] concerning scalar
quadratic BSDEs.
