  Let $(u, \pi)$ with $u=(u_1,u_2,u_3)$ be a suitable weak solution of the
three dimensional Navier-Stokes equations in $\mathbb{R}^3\times [0, T]$.
Denote by $\dot{\mathcal{B}}^{-1}_{\infty,\infty}$ the closure of $C_0^\infty$
in $\dot{B}^{-1}_{\infty,\infty}$. We prove that if $u\in L^\infty(0, T;
\dot{B}^{-1}_{\infty,\infty})$, $u(x, T)\in
\dot{\mathcal{B}}^{-1}_{\infty,\infty})$, and $u_3\in L^\infty(0, T; L^{3,
\infty})$ or $u_3\in L^\infty(0, T; \dot{B}^{-1+3/p}_{p, q})$ with $3<p, q<
\infty$, then $u$ is smooth in $\mathbb{R}^3\times [0, T]$. Our result improves
a previous result established by Wang and Zhang [Sci. China Math. 60, 637-650
(2017)].
