  We obtain new exact solutions in Einstein Gauss-Bonnet gravity of every odd
dimension higher than three. These new spacetimes are stationary but
non-static, coupled with the Maxwell field, and asymptotic AdS at least
locally. In order to investigate such new solutions, we adopt the
characteristic ansatz for the metric form. It is presented that the local
expression of our metric possesses some interesting properties, in which the
most peculiar one is what is called Sasakian structure. Somewhat intricate
relationship is unveiled between our solution and the already-known rotating
solution which has been only one so far in that purely gravitational theory. We
confirm the validity of the rotating spacetime with the evaluation of the
finite angular momentum.
