  Previously, we have presented a framework to use the para-unitary (PU)
matrix-based approach for constructing new complementary sequence set (CSS),
complete complementary code (CCC), complementary sequence array (CSA), and
complete complementary array (CCA). In this paper, we introduce a new class of
delay matrices for the PU construction. In this way, generalized Boolean
functions (GBF) derived from PU matrix can be represented by an array of size
$2\times 2 \times \cdots \times 2$. In addition, we introduce a new method to
construct PU matrices using block matrices. With these two new ingredients, our
new framework can construct an extremely large number of new CSA, CCA, CSS and
CCC, and their respective GBFs can be also determined recursively. Furthermore,
we can show that the known constructions of CSSs, proposed by Paterson and
Schmidt respectively, the known CCCs based on Reed-muller codes are all special
cases of this new framework. In addition, we are able to explain the bound of
PMEPR of the sequences in the part of the open question, proposed in 2000 by
Paterson.
