Erasing a Time Machine Backup

I have been backing up my MBP with Time Machine on my Time Capsule. I also make regular Carbon Copy Cloner Clones. I recently had a problem and recoverd by copying the Clone back to my MBP. When I went to update the Time Machine backup, it did not relate the present data to the previous Time Machine backup. I could just start a new Time Machine backup, but that would leave about 300GB tied up on the old backup. How can I erase the old backup to start over again?