  It is shown that the two remarkable properties of turbulence, the Extended
Self-Similarity (ESS) [R. Benzi {\it et al.}, Phy. Rev. E {\bf 48}, R29,
(1993)] and the She-Leveque Hierarchical Structure (SLHS) [Z.S. She and E.
Leveque, Phy. Rev. Lett. {\bf 72}, 336, (1994)] are related to each other. In
particular, we have shown that a generalized hierarchical structure together
with the most intense structures being shock-like give rise to ESS. Our
analysis thus suggests that the ESS measured in turbulent flows is an
indication of the shock-like intense structures. Results of analysis of
velocity measurements in a pipe-flow turbulence support our conjecture.
