We use a new method to estimate with 5% accuracy the
contribution of pi+on and kaon in-flight-decays to the dimuon data set
acquired with the CDF detector. Based on this improved estimate, we show
that the total number and the properties of the collected dimuon events
are not yet accounted for by ordinary sources of dimuons which also
include the contributions, as measured in the data, of heavy flavor,
$\Upsilon$, and Drell-Yan production in addition to muons mimicked by
hadronic punchthrough.