A memory system comprising a plurality of memory cells each including a storage element having a first terminal and a control terminal. The method for operating the memory system includes applying a first program voltage to control terminals of storage elements and applying a basic reference voltage to first terminals of the storage elements during a first program operation, performing a group verification by comparing threshold voltages of the storage elements with a middle voltage, performing a first program test to check if the threshold voltages of the storage elements are greater than a first programming threshold voltage, and performing a second program operation according to a result of the group verification and a result of the first program test. The middle voltage is smaller than the first programming threshold voltage.