  In this letter we analyse, in the context of the general 2-Higgs Doublet
Model, the structure of the Yukawa matrices, $\widetilde{ \bf Y}_{ _{1,2}
}^{q}$, by assuming a four-zero texture ansatz for their definition. In this
framework, we obtain compact expressions for $\widetilde{ \bf Y}_{ _{1,2}
}^{q}$, which are reduced to the Cheng and Sher ansatz with the difference that
they are obtained naturally as a direct consequence of the invariants of the
fermion mass matrices. Furthermore, in order to avoid large flavour violating
effects coming from charged Higgs exchange, we consider the main flavour
constraints on the off-diagonal terms of Yukawa texture {{$\left(
\widetilde{\chi}_{j}^q \right)_{kl}$}} ($k\neq l$). We perform a $\chi^2$-fit
based on current experimental data on the quark masses and the
Cabibbo-Kobayashi-Maskawa mixing matrix ${ \bf V}_{\rm CKM }$. Hence, we obtain
the allowed ranges for the parameters $\widetilde{ \bf Y}_{ _{1,2} }^{q}$ at
1$\sigma$ for several values of $\tan \beta$. The results are in complete
agreement with the bounds obtained taking into account constraints on Flavour
Changing Neutral Currents reported in the literature.
