The derivation of the method proceeds as follows. First we introduce rank-one (separable)
approximation to the potential
The integral equation for the rank-one part of potential is easily soluble. The full solution of the original problem can therefore be expressed as
in terms of new function . This function is solution of modified Lippmann–Schwinger equation
with 
The remainder potential term  is transparent for incoming wave
i. e. it is weaker operator than the original one.
The new problem thus obtained for  is of the same form as the original one and we can repeat the procedure.
This leads to recurrent relations
It is possible to show that the T-matrix of the original problem can be expressed in the form of chain fraction
where we defined
In practical calculation the infinite chain fraction is replaced by finite one assuming that 
This is equivalent to assuming that the remainder solution
is negligible. This is plausible assumption, since the remainder potential  has all vectors
 in its null space and it can be shown that this potential converges to zero and the chain fraction converges to the exact T-matrix.