The Diels-Alder adduct (-)-5 (a "naked sugar") of furan to 1-cyanovinyl (1R')-camphanate was converted into (+)-(1R,5S,6S,7S)-6-exo,7-exo-(isopropylidenedioxy)-2,8-dioxabicylo[3.2. 1]octan-3-one and into (+)-(1R,5S,6S,7S)-7-endo-(benzyloxy)-6-exo-{[(t-butyl)dimethylsilyl]oxy} -2,8-dioxabicyclo[3.2.1]-octan-3-one ((+)-17). Double methylation at C(4) gave the corresponding 5-deoxy-5-C-dimethyl furanurono-6,1-lactones (+)-42 and (+)-19, respectively. Stereoselective and successive methylation and benzyloxymethylation of (+)-(1R,5S,6S,7S)-6-exo,-7-exo-(isopropylidenedioxy)2,8-dioxabicyclo[3.2 .1]octan-3-one gave (+)-(1R,4R,5S,6S,7S)4-exo-[(benzyloxy)methyl]-6-exo,7-exo-(isopropyliden edioxy)-4-endo-methyl-2,8-dioxabicyclo[3.2.1]octan-3-one ((+)-9). Highly stereoselective oxydative decarboxylation of lactones (+)-9 and (+)-19 led to 5-C-methyl-alpha-beta-D-talo-hexose ((-)-1) and to 6-deoxy-5-C-methyl-alpha-beta-L-arabino-hexose ((-)-2), respectively. Transformation of lactones (+)-9 and (+)-42 into the corresponding acyl azides and their Curtius rearrangements led to (5-ammonio-1,5-N-anhydro-5-deoxy-5-C-methyl-alpha-beta-D-talo-hexitol)-1 -sulfonate ((+)-3) and to (5-ammonio-1,5-N-anhydro-5,6-dideoxy-5-C-methyl-alpha-beta-L-ribo-hexito l)1-sulfonate ((+)-4), respectively.