This paper investigates the consistency property of FC -normal logic program and presents an equivalent deciding condition whether a logic program P is an FC -normal program. The deciding condition describes the characterizations of FC -normal program. By the Petri-net presentation of a logic program, the characterizations of stratification of FC -normal program are investigated. The stratification of FC -normal program motivates us to introduce a new kind of stratification, extended stratification, over logic program. It is shown that an extended (locally) stratified logic program is an FC -normal program. Thus, an extended (locally) stratified logic program has at least one stable model. Finally, we have presented algorithms about computation of consistency property and a few equivalent deciding methods of the finite FC -normal program.