In this paper we establish an improved outer bound on the storage-repair-bandwidth tradeoff of regenerating codes under exact repair.  The result shows that in particular, it is not possible to construct exact-repair regenerating codes that asymptotically achieve the tradeoff that holds under functional repair.   While this had been shown earlier by Tian for the case $[n,k,d]=[4,3,3]$ the present result holds for general $[n,k,d]$.  The new outer bound is obtained by building on the framework established earlier by Shah et al.