A search for the dinucleon decay pp → K+ K+ has been performed using 91.6 kton·yr data from Super-Kamiokande-I. This decay provides a sensitive probe of the R-parity-violating parameter λ112''. A boosted decision tree analysis found no signal candidates in the data. The expected background was 0.28±0.19 atmospheric neutrino induced events and the estimated signal detection efficiency was 12.6%±3.2%. A lower limit of 1.7×10(32) years has been placed on the partial lifetime of the decay O16 → C14K+ K+ at 90% C.L. A corresponding upper limit of 7.8×10(-9) has been placed on the parameter λ112''.