β-Acyclic database scheme has a number of desirable properties, but most former researches about β-acyclic are based on graph theory, without consideration on other canonical properties of database. With the concept of mixed dependency basis, this paper defines the concepts of strict conflict-free and extended strict conflict-free, and proves that decomposition satisfies lossless join, keeps dependency, β-acyclic and 4NF if and only if it is extended strict conflict-free in the mixed environment. Based on this, the paper gives the algorithm for judging strict conflict-free and β-acyclic decomposition in mixed environment, then shows that the complexity of the algorithm is linear using an example based on line graph. This conclusion can directly guide real database designing.