The properties of the set of extended Jordanian twists are studied. It is shown that the boundaries of 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.