  The properties of the set L of extended jordanian twists are studied. It is
shown that the boundaries of L contain twists whose characteristics differ
considerably from those of internal points. The extension multipliers of these
"peripheric" twists are factorizable. This leads to simplifications in the
twisted algebra relations and helps to find the explicit form for coproducts.
The peripheric twisted algebra U(sl(4)) is obtained to illustrate the
construction. It is shown that the corresponding deformation U_{P}(sl(4))
cannot be connected with the Drinfeld--Jimbo one by a smooth limit procedure.
All the carrier algebras for the extended and the peripheric extended twists
are proved to be Frobenius.
