  In [4], the existence of the solution is proved for a scalar linearly growing
backward stochastic differential equation (BSDE) if the terminal value is
$L\exp{\left(\mu \sqrt{2\log{(1+L)}}\,\right)}$-integrable with the positive
parameter $\mu$ being bigger than a critical value $\mu\_0$. In this note, we
give the uniqueness result for the preceding BSDE.
