Construction of monodromy matrix in the F-basis and scalar products in spin chains

We present in a simple terms the theory of the factorizing operator introdu ced recently by Maillet and Sanches de Santos for the spin-1/2 chains. We o btain the explicit expressions for the matrix elements of the factorizing o perator in terms of the elements of the monodromy matrix. We use this resul ts to derive the expression for the general scalar product for the quantum spin chain. We comment on the previous determination of the scalar product of Bethe eigenstate with an arbitrary dual state. We also establish the dir ect correspondence between the calculations of scalar products in the F-bas is and the usual basis.