A Detailed Analysis of a Modified Fritzsch Scheme of Quark Mass Matrices
  We investigate in detail a modified version of the Fritzsch scheme where the diagonal entries $(M_{u,d})_{22}$ are introduced as free parameters instead of being zero. We find that $(M_u)_{22}$ and $(M_d)_{22}$ are restricted to l in the range $m_u-m_c\leq (M_u)_{22}< m_t-m_c$ and $m_d-m_s\leq (M_d)_{22}< m_b-m_s$. In the context of this scheme, we obtain the ratio ${|V_{td}|\over |V_{ts}|}\approx\sqrt{{m_d\over m_s}}$ under quite general conditions whereas the ratio ${|V_{ub}|\over |V_{cb}|}$ is sensitive to the values of $(M_u)_{22}$ and $(M_d)_{22}$. The two independent phases are found to take rather preferred values. 
E. Boridy, C. Hamzaoui, F. Lemay and J. Lindig