Let n and \(\kappa _0\) be positive integers such that \(n>\kappa _0^2+2\) , and let F be a rational proper holomorphic map from the complex unit ball \(\mathbb {B}^n\) into \(\mathbb {B}^N \) with \((\kappa _0 + 1)n + 1 \le N \le (\kappa _0 + 2)n - \kappa _0^2 - 2\) . If the geometric rank of F is \(\kappa _0\) , we prove that F is equivalent to a map of the form \((G, 0, \cdots , 0)\) , where G is a proper holomorphic map from \(\mathbb {B}^n\) into \(\mathbb {B}^{(\kappa _0 + 1)n}\) . Moreover, F is uniquely determined by its 3-jets. A consequence is that every rational proper holomorphic map from \(\mathbb {B}^n\) into \(\mathbb {B}^{4n - 6}\) is determined by its 3-jets.
