We conducted an optical CCD search for supernovae in a sample of 142 bright [ mag], m(B) ≤ 16 nearby ( ) starburst galaxies over the period 1988 December to 1991 June, to a limiting R-band magnitude z ≤ 0.03 of 18. Five supernovae were found, in all cases outside the host galaxy's nucleus. We determine supernova rates (in supernova units or SNU) in the extranuclear regions to be 0.7 h 2 SNU for Type Ia, 0.7 h 2 SNU for Type Ib/ c, and ∼0.6 h 2 SNU for Type II, with large uncertainties but upper

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... limits of 2.2 h 2 , 2.5 h 2 , and 1.7 h 2 SNU, respectively. These rates are similar to those measured in "normal" galaxies. We found no evidence for a supernovainduced brightening in any galactic nucleus and, with a few reasonable assumptions, can place upper limits of 9 h 2 , 12 h 2 , and 7 h 2 SNU on the rates of unobscured supernovae Types Ia, Ib/c, and II, respectively, inside the nuclei.