Several investigations have been done on positive maps on their algebraic structures with more emphasis on completely positive maps. In this study we have described the structure of the Choi matrices for 2−positive maps on positive semidefinite matrices and the conditions for complete positivity of positive linear maps fromMntoMn+1. The motivation behind these objectives is work done by Majewski and Marciniak on the structure of positive mapsφfromMntoMn+1(2≥2) between matrix algebras.