Negative sequential patterns (NSP) referring to both occurring items (positive items) and non-occurring items (negative items) play a very important role in many real applications. Very few methods have been proposed to mine NSP and most of them only mine NSP from frequent positive sequences, not from infrequent positive sequences (IPS). In fact, many useful NSP can be mined from IPS, just like many useful negative association rules can be obtained from infrequent itemsets. e-NSPFI is a method to mine NSP from IPS, but its constraint is very strict to IPS and many useful NSP would be missed. In addition, e-NSPFI only uses a single minimum support, which implicitly assumes that all items in the database are of the similar frequencies. In order to solve the above problems and optimize NSP mining, a 2-level multiple minimum supports (2-LMMS) constraint to IPS is proposed in this paper. Firstly, we design two minimum supports constraints to mine frequent and infrequent positive sequences. Secondly, we use Select Actionable Pattern (SAP) method to select actionable NSP. Finally, we propose a corresponding algorithm msNSPFI to mine actionable NSP from IPS with 2-LMMS. Experiment results show that msNSPFI is very efficient for mining actionable NSP