  It is known that the linear n-setting steering inequalities introduced in
Ref. [Nature Phys. 6, 845 (2010)] are very efficient inequalities in detecting
steerability of the Werner states by using optimal measurement axes. Here, we
construct chained steering inequalities that have improved visibility for the
Werner states under a finite number of settings. Specifically, the threshold
values of quantum violation of our inequalities for the n=4,6,10 settings are
lower than those of the linear steering inequalities. Furthermore, for almost
all generalized Werner states, the chained steering inequalities always have
improved visibility in comparison with the linear steering inequalities.
