Association rule mining techniques are used to search attribute-value pairs that occur frequently together in a data set. Ordinal association rules are a particular type of association rules that describe orderings between attributes that commonly occur over a data set [9]. Although ordinal association rules are defined between any number of the attributes, only discovery algorithms of binary ordinal association rules (i.e., rules between two attributes) exist. In this paper, we introduce the DOAR algorithm that efficiently finds all ordinal association rules of interest to the user, of any length, which hold over a data set. We present a theoretical validation of the algorithm and experimental results obtained by applying this algorithm on a real data set.