Consider two kernel density estimates having the same bandwidth but two different kernels. The criterion which minimizes the L₁ distance between these two estimates is known as the double kernel method. In this work, instead of the L₁ distance, we use the L₂ one. Asymptotic behavior of this criterion and the corresponding bandwidth are investigated. It is shown that the L₂ double kernel method and the least-squares cross-validation technique have almost the same properties. An implementation of the method is also proposed.