The structure of high-lying states in $^{22}$Ne has been studied using the $^{14}$C($^{12}$C,$alpha$)$^{22}$Ne reaction at E($^{12}$C)= 44 MeV. The spins were determined by measuring double ($alpha$,$alpha$) angular correlations. Selective population of the 9$^-$ and 11$^-$ states at E$_x$=20.1 and 20.7 MeV, respectively, identifies those states as the 9$^-$ and 11$^-$ members of the first $K^{pi}$ = 0$^-$ band, whose lower members were investigated by a method using inverse kinematics and a thick gas target. The spin and parity of four other new levels were determined to be 9$^-$ (21.5 MeV),12$^+$ (22.1 MeV),9$^-$ (25.0 MeV) and 8$^+$ (22.9 MeV). The two levels 9$^-$ and 12$^+$ may belong to the rotational doublets.