The weak flavour mixing matrix, appearing in the left-handed charged weak current, is constructed from the Fritzsch mass matrix as functions of six quark masses and three complex phases. On comparing it with the present experimental data on weak flavour mixing, the two complex phases (one taken as zero) seem to be pi /2, for certain quark masses. On the other hand, however, the assumption that the complex phases in the weak flavour mixing matrix are responsible for the weak CP non-conservation implies that the complex phases should be very small for the same quark masses in order to produce the correct magnitude of weak CP non-conservation observed in the neutral kaon system. The discrepancy would not be compromised by varying the quark masses within allowed ranges or by including the long-range contributions to the K0-K0 transition amplitude.