  Context. We highlight the capabilities of the geodetic VLBI technique to test
General relativity in the classical astrometric style, i.e., measuring the
deflection of light in the vicinity of the Sun.
  Aims. In previous studies, the parameter was estimated by global analyses of
thousands of geodetic VLBI sessions. Here we estimate from a single session
where the Sun has approached two strong reference radio sources 0229+131 and
0235+164 at an elongation angle of 1-3 degrees.
  Methods. The AUA020 VLBI session of 1 May 2017 was designed to obtain more
than 1000 group delays from the two radio sources. The Solar corona effect was
effectively calibrated with the dual-frequency observations even at small
elongation from the Sun.
  Results. We obtained with a precision better than what is obtained through
global analyses of thousands of standard geodetic sessions over decades.
Current results demonstrate that the modern VLBI technology is capable of
establishing new limits on observational test of General Relativity.
