It is generally accepted that it is a mistake that Aristotle ignore the moods of the fourth figure in his syllogism. In this paper, I shall argue the Aristotelian syllogism consisting of the essential moods and their derivative moods is complete or self-contained, all the moods of the fourth figure can be derived from the essential moods. The analysis table provided in the paper will contribute to showing the procedure from the essential moods to the derivative ones, and also showing the distinction between the Aristotelian and the traditional syllogism. The traditional syllogism strictly differentiate the major premise from the minor one in a syllogism, and strictly limit the major term and minor one in the premise or the conclusion of a syllogism, and thus some moods described by Aristotle are missing. I think the Aristotelian syllogism is more flexible and feature-rich than the traditional one. If a syllogism contains the negative nouns and the quantified predicates, the number and type of syllogism will be greatly expanded, and can’t be described by the Aristotelian syllogism, let alone the traditional one.