Notes on D-branes of Type IIB String on AdS₅ x S⁵

We promote a study of D-branes of type IIB string on the AdS_5 x S^5 background. The possible D-branes preserving half of supersymmetries were classified up to and including the fourth order of fermionic variable \th in our previous work [hep-th/0310228]. In this paper we show that our classification is still valid even at the full order of \th. This proof supplements our previous results and completes the classification of D-branes in the type IIB string theory on the AdS_5 x S^5.