A very simple proof of the following result is given. Theorem. Let \(f\in L^{\infty}({\mathbb{R}}^ 2)\) and let u be its biharmonic extension to \({\mathbb{R}}_+^ 2\times {\mathbb{R}}_+^ 2\). Then \(| \nabla_ 1\nabla_ 2u|^ 2y_ 1y_ 2dz_ 1dz_ 2\) is a Carleson measure on \({\mathbb{R}}_+^ 2\times {\mathbb{R}}_+^ 2\).