  We prove existence of normalized solutions to \[ \begin{cases} -\Delta u -
\lambda_1 u = \mu_1 u^3+ \beta u v^2 & \text{in $\mathbb{R}^3$} -\Delta v-
\lambda_2 v = \mu_2 v^3 +\beta u^2 v & \text{in
$\mathbb{R}^3$}\int_{\mathbb{R}^3} u^2 = a_1^2 \quad \text{and} \quad
\int_{\mathbb{R}^3} v^2 = a_2^2 \end{cases} \] for any $\mu_1,\mu_2,a_1,a_2>0$
and $\beta<0$ prescribed. The approach is based upon the introduction of a
natural constraint associated to the problem.
  Our method can be adapted to the scalar NLS equation with normalization
constraint, and leads to alternative and simplified proofs to some results
already available in the literature.
