We present the simultaneous observations of the K Ca II 3933.7 Å, H δ 4101.7 Å and He I 4471.5 Å lines in the limb solar flare of July 17, 1981. For two moments of the flare we analyzed Stokes I ± V and V profiles of these lines from observations made on the Echelle spectrograph of the horizontal solar telescope of the Astronomical Observatory of Taras Shevchenko National University of Kiev. In the flash phase of the flare, all named lines had very wide emissions, with a wing length of 6-8 Å. An interesting feature was observed in the violet wings of these lines, namely, narrow emission peaks with a width of only 0.25-0.35 Å. The Zeeman splitting of these emission peaks correspond to magnetic field strength in range 1300-2900 G at altitudes of 10-15 Mm above the level of the photosphere. Magnetic fields of 'kilogauss' range (up to 3200 G) were found for some locations also in post-peak phase of the flare. Likely, the true local magnetic fields in the flare could be even larger, since the obtained results represent a longitudinal component of the magnetic field assuming that the filling factor equals unity. A new indication of the existence of superstrong magnetic fields follows from a comparison of the kinetic temperatures and turbulent velocities found from the narrow emission component in the flash phase of the flare. Considering this emission component to be optically thin, we found that there is an anti-correlation between temperature and turbulent velocity. Such a dependence seems unlikely and, possibly, the widths of the line profiles reflect, in our case, not turbulent velocities, but very strong magnetic fields. The corresponding estimates of the magnetic field by the K Ca II line lead to the value B = 8.3 kG, and by the He I 4471.5 line -to the value B = 6.7 kG. Considering that the He I line is clearly closer to the case of an optically thin layer, the closeness of these estimates is very encouraging. Our results are apparently the first indications of superstrong magnetic fields of 6-7 kG at an altitude of about 10 Mm in a solar flare.