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We emphasise that even in the extreme chiral limit where only the top andbottom quarks acquire mass, quark mixing is physically meaningful. This impliesthat the natural value of $|V_{13}|^2 + |V_{23}|^2$ is of order one, which isto be compared to its experimental value of order $10^{-3}$ . We show how thisfine-tuning problem of the Standard Model can be solved through an extension ofthe Standard Model where vector-like quarks and a complex singlet areintroduced, together with a flavour symmetry. The mixings of the light quarksare generated through the mixing of the vector-like quarks with the standardquarks.

Solving a Fine-Tuning Problem of the Standard Model through the Introduction of Vector-Like Quarks