  Serious difficulties arise in the construction of chains of twists for
symplectic Lie algebras. Applying the canonical chains of extended twists to
deform the Hopf algebras U(sp(N)) one is forced to deal only with improper
chains (induced by the U(sl(N)) subalgebras). In the present paper this problem
is solved. For chains of regular injections the sets of maximal extended
jordanian twists F_{E,k} are considered. We prove that there exists for
U(sp(N)) the twist F_{B,k} composed of the factors F_{E,k}. It is demonstrated
that the twisting procedure deforms the space of the primitive subalgebra
sp(N-1). The recursive algorithm for such deformation is found. This
construction generalizes the results obtained for orthogonal classical Lie
algebras and demonstrates the universality of primitivization effect for
regular chains of subalgebras. For the chain of maximal length the twists
F_{B,k,max} become full, their carriers contain the Borel subalgebra B(sp(N)).
Using such twisting procedures one can obtain the explicit quantizations for a
wide class of classical r-matrices. As an example the full chain of extended
twists for U(sp(3)) is considered.
