1Department of Mathematics, Faculty of Basic Sciences, University of Mazandaran, P. O. Box 47416-1468, Babolsar, Iran.
2Department of Mathematics, Faculty of Basic Sciences, Yasouj University, P. O. Box 75918-74831, Yasouj, Iran.
In this paper we show that if A is a unital Banach algebra and B is a purely innite C*-algebra such that has a non-zero commutative maximal ideal and $\phi:A \rightarrow B$ is a unital surjective spectrum preserving linear map. Then $\phi$ is a Jordan homomorphism.