The shadow minimization problem for t-intersecting systems of finite sets is considered. Let $ {\user1{A}} $ {\user1{A}} be a family of k-subsets of $ {\user1{A}} $ {\user1{A}} is the set of all (k-$ \partial _{{\ell }} {\user1{A}} $ \partial _{{\ell }} {\user1{A}} contained in the members of $ {\user1{A}} $ {\user1{A}} . Let $ {\user1{A}} $ {\user1{A}} be a t-intersecting family (any two members have at least t elements in common) with $ {\left| {\user1{A}} \right|} = m $ {\left| {\user1{A}} \right|} = m . Given k,t,m the problem is to minimize $ {\left| {\partial _{{\ell }} {\user1{A}}} \right|} $ {\left| {\partial _{{\ell }} {\user1{A}}} \right|} (over all choices of $ {\user1{A}} $ {\user1{A}} ). In this paper we solve this problem when m is big enough.