No you will have to snap your time range to the minute (or the hour, day, etc...)
example : earliest=-20m@m latest=-1m@m
then the results will still be valid for the next minute.
see http://docs.splunk.com/Documentation/Splunk/4.3.4/User/ChangeTheTimeRangeOfYourSearch#Specify_relative_time_ranges_in_your_search
It is more useful for longer periods, by example (earliest=-20m@m latest=-5m@m, and have it run every 5 min)
If you really want to update every minutes, then it will have to run every minute...
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