  Borsuk conjectured that every n-dimensional bounded set of positive diameter
can be partitioned into n+1 sets of smaller diameters. This conjecture was
proved for n=2 by Borsuk, for n=3 first by Eggleston, and disproved for n > 297
by Hinrichs and Richer. It is not known if the conjecture holds for 3 < n <
298. The best upper bound for the number of subsets of smaller diameters a
four-dimensional set can be partitioned into is nine. This estimate was given
by Lassak in 1982. In this note we improve this estimate by one.
