The generalization of abelian Higgs vortices to the non-abelian case has recently gained much attention. They may play important role in understanding confinement in QCD, for instance. Witten has discovered that axially symmetric (SO(3) invariant) instantons in SU(2) gauge group can be mapped to U(1) vortices on a hyperbolic plane. This dimensional reduction allowed exact solutions for vortices. We have found a new dimensional reduction of SO(3) invariant instantons in SU(2N) gauge group to obtain non-Abelian vortices of SU(N)xSU(N)xU(1) gauge group on the hyperbolic plane. We have obtained a class of exact solutions for U(1)^N subgroup. Orientational moduli of the non-abelian vortices are still to be worked out.