We discuss a new mass matrix with specific texture zeros for the quarks. The three flavor mixing angles for the quarks are functions of the quark masses and can be calculated. The following ratios among CKM matrix elements are given by ratios of quark masses: |Vtd/Vts| q md /ms and |Vub/Vcb| p mu/mc . Also we can calculate two CKM matrix elements: |Vcb| |Vts| 2 (ms/mb ). This relation as well as the relation |Vtd/Vts| q md /ms are in good agreement with the experimental data. There is a problem with the relation |Vub/Vcb| p mu/mc , probably due to wrong estimates of the quark masses mu and m
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