A highly stereoselective synthesis of the key intermediate $\underline{99}$ of 1-$\beta$-methylcabapenem antibiotics was accomplished in overall 14 steps in 8 reaction pots starting from commercially available (R)-(-)-3-bromo-2-methyl-1-propanol $\underline{67}$. Starting alcohol $\underline{71c}$ was readily obtained from trimethylsilyl ether of $\underline{67}$ in one pot reaction in 51\% overall yield. Alcohol $\underline{71c}$ was subjected to Swern oxidation followed by nitrone formation with N-benzylhydroxylamine and 1,3-dipolar cycloaddition effected the formation of isoxazolidine $\underline{93a}$ in 71\% overall yield with high diastereoselectivity(24:1). Deacetylation, oxidation, enol ether formation and catalytic osmylation in sequence provided $\alpha$-hydroxy ketone $\underline{98}$ in 70\% overall yield. $\underline{98}$ was subjected to oxidative cleavage and reduction followed by cyclization in one pot to furnish the desired key intermediate to 1-$\beta$-methylcabapenem 2, N-benzylated azetidinone $\underline{99}$ in 57\% overall yield.