How to fix IndexMissingException

I recently ran into an issue where my cluster is reporting an
IndexMissingException. I tried deleting the faulty index, but I keep
getting the same error returned. How do I fix this problem?

$ curl -XDELETE 'http://localhost:9200/logstash-2014.09.04.11'

{"error":"IndexMissingException[[logstash-2014.09.04.11]
missing]","status":404}

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