The number of frequent itemsets is often too large to handle, so it is very necessary to work out a condensed representation of the collection of all frequent itemsets. In this paper, we propose a new condensed representation called frequent non-almost-derivable itemsets. This representation is a subset of the original collection of frequent itemsets. For any removed itemset X(which is called an frequent almost-derivable itemset), we can derive a lower and an upper bound of its support from this representation, and the lower bound and the upper bound is close enough(can be controlled by a userdefined parameter). We also propose an Apriori-like algorithm, which can extract all frequent nonderivable itemsets. Extensive empirical results on real datasets show the compactness and good approximation of this representation.