Negative frequent itemsets (NFIS) like (a1a2¬a3a4) have played important roles in real applications because we can mine valued negative association rules from them. In one of our previous work, we proposed a method, namede-NFISto mine NFIS from positive frequent itemsets (PFIS). However,e-NFISonly uses single minimum support, which implicitly assumes that all items in the database are of the same nature or of similar frequencies in the database. This is often not the case in real-life applications. So a lot of methods to mine frequent itemsets with multiple minimum supports have been proposed. These methods allow users to assign different minimum supports to different items. But these methods only mine PFIS, doesn’t consider negative ones. So in this paper, we propose a new method, namede-msNFIS, to mine NFIS from PFIS based on multiple minimum supports. E-msNFIScontains three steps: 1) using existing methods to mine PFIS with multiple minimum supports; 2) using the same method ine-NFISto generate NCIS from PFIS got in step 1; 3) calculating the support of these NCIS only using the support of PFIS and then gettingNFIS. Experimental results show that thee-msNFISis efficient.