Consider a manifold \(M\) of dimension \(2n\) without boundary with an exact symplectic form \(\omega\). Exactness means that there is a primitive \(\theta_{0}\), a \(1\)-form with \(d\theta_{0}=\omega\). The author constructs a nowhere vanishing primitive \(\theta\) of the symplectic form \(\omega\). First, choose an exhaustive Morse function \(\gamma:M\to \mathbb{R}_{>0}\) on the manifold \(M\) (i.e., such that \(\gamma^{-1}((-\infty,c])\) are compact for all \(c\in \mathbb{R}\)). For each isolated critical point \(z\) of \(\gamma\), choose a contractible open neighborhood \(U_{z}\), small enough so that such open neighborhoods of critical points do not intersect each other. Then one can choose global functions \(x_{i}\), \(i\in\{1,2,\dots,2n\}\) satisfying that all the \(x_{i}\)’s vanish at the critical points and \(\omega=2\cdot \sum_{i=1}^{n}dx_{i}\wedge dx_{i+n}\) on the neighborhoods of the critical points. Locally on each neighborhood \(U_{z}\), the \(1\)-form \[\tau_{z}:=\sum_{i=1}^{n}x_{i}dx_{i+n}-\sum_{i=1}^{n}x_{i+n}dx_{i}\] satisfy \(d\tau_{z}=\omega|_{U_{z}}\). Since the symplectic form \(\omega\) is exact, there is a primitive \(\theta_{0}\) with \(d\theta_{0}=\omega\). Applying bump functions on \(U_{z}\), one can construct another primitive \(\theta_{1}\) of \(\omega\), satisyfing \(\theta_{1}|_{U_{z}}=\tau_{z}\) near the neighborhoods of critical points. The next step is to modify the Morse function \(\gamma\) to \(\widetilde{\gamma}\) preserving the properties constructed as above and satisfying that locally near the critical points \[d\widetilde{\gamma}=2\cdot \sum_{i=1}^{s_{z}}x_{i}dx_{i}-2\cdot \sum_{i=s_{z}+1}^{2n}x_{i}dx_{i}\] as well as \[\theta_{1}=\sum_{i=1}^{n}x_{i}dx_{i+n}-\sum_{i=1}^{n}x_{i+n}dx_{i}.\] Here, \(s_{z}\) is the index of \(z\) defined as \[\gamma(y)=\sum_{i=1}^{s_{z}}y_{i}^{2}-\sum_{i=s_{z}+1}^{2n}y_{i}^{2}+\gamma(z)\] on a relatively compact open neighborhood of \(z\) contained in \(U_{z}\). Moreover, there is a constant \(K_{0}>0\) such that for all \(K\geq K_{0}\), the primitive \(\theta_{1}+K\cdot d\widetilde{\gamma}\) that vanishes near the critical points, actually vanishes exactly at the critical points. One can modify the Morse function \(\widetilde{\gamma}\) so that the primitive vanishes exactly at the critical points. The final step consists of moving away these isolated zeroes of the primitive by induction and applying the construction of symplectomorphism in [W. M. Boothby, Trans. Am. Math. Soc. 137, 93–100 (1969; Zbl 0181.49503)].