We study the fourth-order nonlinear Schrödinger equations \(\begin{aligned} \left\{ \begin{array}{c} i\partial _{t}u+\frac{1}{2}\partial _{x}^{2}u-\frac{1}{4}\partial _{x}^{4}u=t^{\nu }\overline{u}^{3},\,\,t\textbf{,}x\in \mathbb {R}, \\ u\left( 0,x\right) =u_{0}\left( x\right) ,\,\,x\in \mathbb {R}, \end{array} \right. \end{aligned}\) where \(0\le \nu <\frac{1}{16},\) the initial data \(u_{0}\left( x\right) \) are odd. Nonlinearities of the form \(t^{\nu }\overline{u}^{3}\) with \(\nu >0\) are expected to be subcritical, in the sense that the asymptotic behavior of solutions are different from that of the linear problem. We prove that this is not true under the conditions such that \(0\le \nu <\frac{1}{16}\) in the case of the initial data are the odd functions.
