The present paper gives some results on local minimum and orthogonality of normal derivations in Cp-Classes. We employ some techniques for normal derivations due to Mecheri, Hacene, Bounkhel and Anderson. Let CpCp be normal, then the linear map = attains a local minimum at x Cp if and only if z Cp such that ) Also let Cp, and let have the polar decomposition, then the map attains local minimum on Cp at T if and only if. Regarding orthogonality, let SCp and let N(S) have the polar decomposition N(S)=U|N(S)|, thenfor XCp if . Moreover, the map has a local minimum at x if and only if for y.