  Every nonsingular fermion mass matrix, by an appropriate unitary
transformation of right-chiral fields, is equivalent to a triangular matrix.
Using the freedom in choosing bases of right-chiral fields in the minimal
standard model, reduction to triangular form reduces the well-known ambiguities
in reconstructing a mass matrix to trivial phase redefinitions. Furthermore,
diagonalization of the quark mass sectors can be shifted to one charge sector
only, without loosing the concise and economic triangular form. The
corresponding effective triangular mass matrix is reconstructed, up to trivial
phases, from the moduli of the CKM matrix elements, and vice versa, in a unique
way. A new formula for the parametrization independent CP-measure in terms of
observables is derived and discussed.
