  Verification of theoretical predictions of an oscillating behavior of the
fine-structure constant, alpha, with cosmic time requires high precision
measurements at individual redshifts, while in earlier studies the mean Delta
alpha/alpha values averaged over wide redshift intervals were usually reported.
This requirement can be met via the Single Ion Differential alpha Measurement
(SIDAM) procedure. We apply SIDAM to the FeII lines associated with the damped
Ly-alpha system observed at z=1.15 in the spectrum of HE0515-4414. The weighted
mean calculated on base of carefully selected 34 FeII pairs is <Delta
alpha/alpha>=(-0.07+/-0.84)10^{-6}. The precision of this estimate represents
the absolute improvement with respect to what has been done in the measurements
of Delta alpha/alpha.
