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Based on the structure of non-full-$3$-rank $STS(3^k)$ and the orthogonalLatin squares, we mainly give sufficient conditions for $STS(3^k)$ of $3$-rank$\leq 3^k-r$ to be resolvable in the present paper. Under the conditions, theblock set of $STS(3^k)$ can be partitioned into $\frac{3^k-1}{2}$ parallelclasses, i.e., $\frac{3^k-1}{2}$ $1$-$(v,3,1)$ designs. Finally, we prove that$STS(3^k)$ of 3-rank $\leq 3^k-r$ is resolvable under the sufficientconditions.

Sufficient conditions for STS$(3^k)$ of 3-rank $\leq 3^k-r$ to be resolvable