The F-function is the main part of the Camellia algorithm, used in encryption, decryption and key expansion. In this paper, the construction and properities of the F-function, especially the S-function in the F-function, are studied. A more detailed description of the S-function is given, which is more conducive to the understanding of the S-function look-up table. And the avalanche property of the S-box is also tested, which confirms that the S-box meets the strict avalanche criterion basically.