  The MSS-sequences (U-sequences) in a wide class of unimodal maps have the
look $\mathrm{P}=(\mathrm{R} \mathrm{L}^{q})^{n_1} \mathrm{S}_1(m_1,q-1)
(\mathrm{R} \mathrm{L}^{q})^{n_2}\mathrm{S}_2(m_2,q-1) $ $\ldots$ $ (\mathrm{R}
\mathrm{L}^{q})^{n_r}$ $ \mathrm{S}_r(m_r,q-1)\mathrm{C},$ where
$\mathrm{S}_i(m_i, q-1)$ are sequences of $\mathrm{R}$s and $\mathrm{L}$s that
contain at most $q-1$ consecutive $\mathrm{L}$s. The first block
$\mathrm{RL}^q$ and the sequence $\mathrm{S}_1$ following it are essential for
an admissible sequence to be a MSS-sequence. Moreover $\mathrm{S}_i(m_i,q-1), \
i=2, \ldots, r$ are determined by $\mathrm{S}_1(m_1,q-1)$. Explicit structure
of MSS-sequences will be given as well as the theorems that decompose the
non-primary MSS-sequences. The cardinality will be calculated for some
important sets of non-primary MSS-sequences and an algorithm to generate the
blocks $\mathrm{S}_i(m_i,q-1), \ i=1, \ldots, r$ will be provided, as the
construction of the blocks $\mathrm{S}_i(m_i,q-1)$ allows the construction of
the MSS-sequences.

Dynamical Systems