We present a new block cipher called DyC. It consists of four sets (procedures) having the different $2^2,;2^2,;2^4$, and $2^8$ one-to-one correspondence functions as the elements. The round key is used to determine exactly one composite function from the possible $2^{16}$ composite functions. DyC supports 8 $ imes$ n bit key size, 16 $ imes$ m bit block length, and n rounds. We have confirmed that DyC offers security against other well-known advanced cryptanalytic attacks including the slide attacks and interpolation attacks. In this paper, we show several properties of the key schedule of DyC by mathematical analysis.