Abstract: Being a kind of important acyclic degrees, β acyclic has become basic demand of normalization with lossless join, keep dependency and 4NF under MVD environment, and can guide directly database schema design. In this paper, the concept of strictly conflict free is given, and using the line graph as tools, it is certified that line graph of a database schema and its duplicate reduced sub graph are triangulated, and every triangle in line graph is compatible. Database schema is decomposed from a strictly conflict free MVD set by using a decomposition trees algorithm. It is concluded that the sufficient and necessary condition of database schema decomposition satisfying lossless join, keep dependency, 4NF, and β acyclic under conflict\|free condition is that the MVD sets have a strictly conflict free cover.