This paper is devoted to studying the Cauchy problem for the Ostrovsky equation $$\begin{aligned} \partial _{x}\left( u_{t}-\beta \partial _{x}^{3}u +\frac{1}{2}\partial _{x}(u^{2})\right) -\gamma u=0, \end{aligned}$$with positive \(\beta \) and \(\gamma \). This equation describes the propagation of surface waves in a rotating oceanic flow. We first prove that the problem is locally well-posed in \(H^{-\frac{3}{4}}(\text{ R })\). Then we reestablish the bilinear estimate, by means of the Strichartz estimates instead of calculus inequalities and Cauchy–Schwartz inequalities. As a byproduct, this bilinear estimate leads to the proof of the local well-posedness of the problem in \(H^{s}(\text{ R })\) for \( s>-\frac{3}{4}\), with help of a fixed point argument.