A Remark on Schimmerling's Question

Schimmerling asked whether square(lambda)* + GCH entails the existence of a lambda(+)-Souslin tree, for a singular cardinal lambda. We provide an affirmative answer under the additional assumption that there exists a non-reflecting stationary subset of E-not equal cf(lambda)(lambda+). As a bonus, the outcome lambda(+)-Souslin tree is moreover free.