  Verification of theoretical predictions of an oscillating behavior of the
fine-structure constant alpha with cosmic time requires high precision Delta
alpha/alpha 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 proposed in Levshakov et al. (2005). We
apply the 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 <Delta
alpha/alpha> calculated on base of carefully selected 34 FeII pairs {1608,X} (X
= 2344, 2374, and 2586 A) is <Delta alpha/alpha> = (-0.07+/-0.84) 10^{-6}
(1sigma C.L.). The precision of this estimate improves by a factor 2 the
previous one reported for the same system by Quast et al. (2004). The obtained
result represents an absolute improvement with respect to what has been done in
the measurements of Delta alpha/alpha.
