The authors look at ordinal potential games originally defined by \textit{D. Monderer} and \textit{L. S. Shapley} [Games Econ. Behav. 14, 124-143 (1996; Zbl 0862.90137)]. As opposed to the original definition using potential functions (into the real numbers), this paper defines potential ordinal games using arbitrary preorders. \textit{M. Voorneveld} and \textit{H. Norde} [Games Econ. Behav. 19, 235-242 (1997; Zbl 0882.90135)] proved a characterization result for potential ordinal games in the original Monderer-Shapley context. The Monderer-Shapley approach required them to assume that the sets of strategies are countable in order to prove their characterization result (they give a counterexample for the uncountable case). Replacing the potential functions of Monderer and Shapley in the definition by preorders (not necessarily embeddable into the real numbers) allows the authors in this paper to get rid of the additional assumption that the strategy sets are countable. The above mentioned Voorneveld-Norde example without potential function has a potential preorder in the Norde-Patrone sense that is not embeddable into the real numbers.