On the basis of studying the completely preserving idempotency maps and by using the method of operator algebra

additive maps of completely preserving skew idempotency between standard operator algebras on real or complex infinite dimensional Banach spaces was discussed.By means of the conversion from the above problems to ones of maps preserving zero sets on rank one idempotent sets

it is proved that all the completely preserving skew idempotency additive maps between standard operator algebras are isomorphism or(in the complex case) conjugate-isomorphism.