Degree of a holomorphic map between unit balls from $\mathbb{C}^2$ to $\mathbb{C}^n$

Let $f$ be a rational proper holomorphic map between the unit ball in $\mathbb{C}^2$ and the unit ball in $\mathbb{C}^n.$ Write

$f=\dfrac{(p_1, \dots, p_n)}{q},$

where $p_j, j=1, \dots,n,$ and $q$ are holomorphic polynomials, with $(p_1,\dots,p_{n},q)$ $=1.$ Recall that the degree of $f$ is defined by

   deg$f =$$\text {max}\{\text{deg} (p_j)_{j=1,\dots,n}, \text{deg} q\}.$

In this paper, we give a bound estimate for the degree of $f,$ improving the bound given by Forstneric (1989).