We report a measurement of the relative branching ratio of two Cabibbo
-suppressed decay modes: D0 --> pi-pi+ and D0 --> K-K+ . The data were
accumulated in the 1990-1991 fixed target run of Fermilab high energy
photoproduction experiment E687. The branching ratios of these modes
relative to the Cabibbo-allowed decay DO --> K-pi+ are also presented.
The relative branching ratios are measured to be GAMMA(D0 --> KK)/GAM
MA(D0 --> pipi) = 2.53 +/- 0.46 +/- 0.19, GAMMA(D0 --> KK)/GAMMA (D0 -
-> Kpi) = 0.109 +/- 0.007 +/- 0.009, and GAMMA(D0 --> pipi)/GAMMA (D0
--> Kpi) = 0.043 +/- 0.007 +/- 0.003.