  In a series of papers, we developed a technique for estimating the inner
eccentricity in hierarchical triple systems, with the inner orbit being
initially circular. However, for certain combinations of the masses and the
orbital elements, the secular part of the solution failed. In the present
paper, we derive a new solution for the secular part of the inner eccentricity,
which corrects the previous weakness. The derivation applies to hierarchical
triple systems with coplanar and initially circular orbits. The new formula is
tested numerically by integrating the full equations of motion for systems with
mass ratios from 10^(-3) to 10^(3). We also present more numerical results for
short term eccentricity evolution, in order to get a better picture of the
behaviour of the inner eccentricity.
