  Inspired by the experimental report by WASA-at-COSY Collaboration, we
investigate the possibile existence of the dibaryon candidate $N\Delta$ with
quantum numbers $IJ^P=21^+$ ($D_{21}$). The dynamical calculation shows that we
cannot obtain the bound $D_{21}$ state in the models which can obtain the
experimental $d^{*}$. %although the $D_{21}$ state can bound in the range of
parameters in quark models. The low-energy scattering phase shifts of the
$N-\Delta$ scattering give the same conclusion. Besides, the mass calculation
by using the Gursey-Radicati mass formula and the analysis of the matrix
elements of the color magnetic interaction show that the mass of $D_{21}$ is
larger than that of $D_{12}$ ($N\Delta$ with $IJ^P=12^+$), which indicate that
it is less possible for the $D_{21}$ than the $D_{12}$ to form bound state.
