It has been established that the preliminary treatment of gamma-Al2O3 with acid or trialkylborate increases the activity of an alumina-rhenium catalyst roughly by a factor of 2-15, with retention of high selectivity. The Re2O7 content of the catalyst can be reduced in this case from 15 to 2.5-5.0 wt.%. The introduction of oxides of variable-valency metals (Mo or V) into the catalyst also enables its activity to be increased.