The conditions of positive D-type map Φπ1

π2constructed from a pair of permutations{π1

π2}on 4×4 matrix algebras was investigated.For a permutation pair{π1

π2}of(1

2

3

4)

a notion of property(C)was introduced.A necessary and sufficient condition for{π1

π2}with the property(C)was obtained. Applying two lemmas

it is shown that

if{π1

π2}has the property(C)

then theD-type map Φπ1

π2 on 4× 4 matrix algebras constructed from{π1

π2}is positive

which proposes a new method to construct positive maps and may be applied to detect the entanglement in the quantum states of 44 composite systems.