A combination of closed sequential pattern mining and closed itemset pattern mining was proposed to mine closed multidimensional sequential patterns. There are two ways for this combination; (1) mining closed itemset patterns from multidimensional information followed by mining closed sequential patterns from sequences associated with closed itemset patterns, and (2) mining closed sequential patterns from sequences followed by mining closed itemset patterns from multidimensional information associated with closed sequential patterns. In the first way the major cost is mining all sequences associated with closed itemset patterns. A similar problem occurs with the second way, the major cost is mining all multidimensional information associated with closed sequential patterns. Therefore, this paper proposes two new combinations that don't need to mine all sequences in the first combination, and all multidimensional information in the second combination. Both combinations can be effected by exploiting two concepts. In the first combination, any closed sequential patterns associated with a closed itemset patten I can be found from a set of closed sequential patterns associated with a closed itemset pattern I' if I sup I'. In the second combination, any closed itemset patterns associated with a closed sequential pattern s can be found from a set of closed sequential patterns associated with a closed itemset pattern s' if s sup s'.