Bypassed, Empty Relay Log
You be able to delete it without issues. Why ?

Look for the file relay-log.index and display it

# cat relay-log.index


You will see a list of relay logs MySQL Replication needs and rotates. If relay.000724 is not in relay.index, you can delete relay.000724 without breaking anything.

Why is is still around ? It could be anything. Between setting up replication after an outrage, skipping SQL Errors, and just plain Starting and Stopping, along with a low expire_logs_days could leave one or more relay logs lingering.

In light of these things, if a relay log does not appear in relay.index, you can delete it.

Why is the relay log so empty ?

It has to do with the mechanism Replication uses to rotate to the next relay log. You will not see these annoying little files very often. The only time I usually see them is with one of the following:


when the SQL thread is broken
when the SQL thread is extremely busy with a long running query


In either case, the IO thread keeps collecting binlog events. Instead of triggering a rotation when the relay log reaches 1G or whatever max_binlog_size or max_relay_log_size is, two little relay logs with nothing in them mark the place where a rotation would have occurred.

UPDATE 2014-07-21 15:28 EDT

Since the relay-log.index both relay logs, there are one of two things you could do:


Leave it alone and let MySQL Replication rotate it away on its own
Reset all the relay logs back to relay-log.000001 with the following

Run STOP SLAVE;
Run SHOW SLAVE STATUS\G
Find Relay_Master_Log_File in the Status (say it is mysql-bin.001234)
Find Exec_Master_Log_File in the Status (say it is 123789456)
Run CHANGE MASTER TO MASTER_LOG_FILE='mysql-bin.001234',MASTER_LOG_POS=123789456;
Run START SLAVE;