  I define a set of conditions that the most general hierarchical Yukawa mass
matrices have to satisfy so that the leading rotations in the diagonalization
matrix are a pair of (2,3) and (1,2) rotations. In addition to Fritzsch
structures, examples of such hierarchical structures include also matrices with
(1,3) elements of the same order or even much larger than the (1,2) elements.
Such matrices can be obtained in the framework of a flavor theory. To leading
order, the values of the angle in the (2,3) plane (s_{23}) and the angle in the
(1,2) plane (s_{12}) do not depend on the order in which they are taken when
diagonalizing. We find that any of the Cabbibo-Kobayashi-Maskawa matrix
parametrizations that consists of at least one (1,2) and one (2,3) rotation may
be suitable. In the particular case when the s_{13} diagonalization angles are
sufficiently small compared to the product s_{12}s_{23}, two special CKM
parametrizations emerge: the R_{12}R_{23}R_{12} parametrization follows with
s_{23} taken before the s_{12} rotation, and vice versa for the
R_{23}R_{12}R_{23} parametrization.
