Yes! The spelling of argument does not follow the common patterns for adding a suffix. Spelling Rule 13 says to drop the silent E when adding a VOWEL suffix. We don't normally drop the silent E when adding a consonant suffix.
Argument is completely decodable; its spelling make sense with all the other rules, because the U can say its long sound at the end of the syllable. But it is an exception to the normal suffixing patterns described in the suffixing rules.
About 2% of English words overall contain something that breaks the rules. The suffixing rules have more exceptions than most of the rules, but it's still a small percentage overall.