least by $\epsilon ^{2}$ ($\epsilon =\bar{\varepsilon},\varepsilon $ for $Y=Y_{d},Y_{u}).$ There is an exception to this conclusion if $Y_{23}$ does not preserve the hierarchical structure and is of ${\mathcal{O}}(1)$ saturating the bound in Eq. (\[genform\]). In this case it is possible that $N_{23}^{R}={\mathcal{O}}(1)$ and therefore corrections ${\mathcal{O}}(1)$ to $Y_{i3}$ are still possible. Even in this case, it is clear that we can never modify the order in $\epsilon $ of the different elements of the Yukawa matrix, all it can do is to change the ${\mathcal{O}}(1)$ coefficients of the $Y_{i3}$ elements. To determine whether this special case is possible one needs to know $Y_{32}$ and this can be done through measurement of flavour changing neutral currents [@FCNC; @b2s] or lepton flavour violation [@LFV].

Thus, using the triangular form, we have shown that the Kähler corrections to the Yukawa matrix are sub-dominant for hierarchical Yukawa matrices. In the next section we prove that this is also true for the observable mixing angles and mass eigenstates.

###  Additional texture zeros

A special situation occurs when one of $a,b,c,d$ is $<{\mathcal{O}}(1)$ giving rise to an approximate texture zero. This can spoil the hierarchical structure of our Yukawa textures, $Y_{kj}<Y_{ij}$ for $i>k$ and $\ j\geq 