  The goal of this note is to construct a uniformly antisymmetric function
f:R-> R with a bounded countable range. This answers Problem 1(b) of Ciesielski
and Larson. (See also list of problems in Thomson and Problem 2(b) from
Ciesielski's survey.) A problem of existence of uniformly antisymmetric
function f:R-> R with finite range remains open.
