  Recently, Cristofaro-Gardiner and Hutchings proved that there exist at least
two closed characteristics on every compact star-shaped hypersuface in ${\bf
R}^4$. Then Ginzburg, Hein, Hryniewicz, and Macarini gave this result a second
proof. In this paper, we give it a third proof by using index iteration theory,
resonance identities of closed characteristics and a remarkable theorem of
Ginzburg et al.
