The acid-catalyzed rearrangement of bi- and tricyclic cyclobutyl ketones 8–20 having a bicyclo[4.2.01octan-2-one moiety with AlCl3 was studied to elucidate the scope and limitations of the novel rearrangement by which the tricyclic ketone 1 gave the angularly fused triquinane ketone 2. 5- or 6-methylbicyclo[4.2.0]octan-2-ones (8 and 9) did not rearrange. 5,6-Disubstituted bicyclo[4.2.0]octanones 10–18 without methyl substituent at C(1) rearranged smoothly via the new-type pathways to give diquinane derivatives 23–32. Ketones 19 and 20 having a C(1) methyl group of the bicyclo[4,2.0] unit rearranged through the Cargill-type pathway to give bicyclo[3.2.1]octan-8-one derivatives 33 and 35 and the diquinane ketone 34. Tetracyclic ketone 21 and bicyclo[5.2.0]nonan-2-one derivative 22 also rearranged via the new-type pathway to give the tetraquinane ketone 36 and homotriquinane 37. A plausible reaction mechanism for the novel rearrangement is proposed which involves the fission of the central cyclobutane bond to generate the homoallylcarbinyl cation 43 (path g) as the primary process followed by the 1,2-hydride shift (path h) and the subsequent transannular cyclization (path i) of the cation 44 to the product. With this rearrangement as the key step, the facile total syntheses of the angularly fused triquinane natural products (±)-5-oxosilphiperfol-6-ene (5) and (±)-silphiperfol-6-ene (6) were performed.