  We consider a mass-critical system of nonlinear Sch\"{o}dinger equations
\begin{align*} \begin{cases} i\partial_t u +\Delta u =\bar{u}v,\\ i\partial_t v
+\kappa \Delta v =u^2, \end{cases} (t,x)\in \mathbb{R}\times \mathbb{R}^4,
\end{align*} where $(u,v)$ is a $\mathbb{C}^2$-valued unknown function and
$\kappa >0$ is a constant. If $\kappa =1/2$, we say the equation satisfies
mass-resonance condition. We are interested in the scattering problem of this
equation under the condition $M(u,v)<M(\phi ,\psi)$, where $M(u,v)$ denotes the
mass and $(\phi ,\psi)$ is a ground state. In the mass-resonance case, we prove
scattering by the argument of Dodson \cite{MR3406535}. Scattering is also
obtained without mass-resonance condition under the restriction that $(u,v)$ is
radially symmetric.
