Using data from the FOCUS (E831) experiment at Fermilab, we present a new measurement for the branching ratios of the Cabibbo-suppressed decay modes D0→π−π+ and D0→K−K+. We measured: Γ(D0→K−K+)/Γ(D0→π−π+)=2.81±0.10(stat)±0.06(syst), Γ(D0→K−K+)/Γ(D0→K−π+)=0.0993±0.0014(stat)±0.0014(syst), and Γ(D0→π−π+)/Γ(D0→K−π+)=0.0353±0.0012(stat)±0.0006(syst). These values have been combined with other experimental data to extract the ratios of isospin amplitudes and the phase shifts for the D→KK and D→ππ decay channels
