The problem of finding a largest stable matching where preference lists may include ties and unacceptable partners (MAX SMTI) is known to be NP-hard. It cannot be approximated within $33/29 \ (>1.1379)$ unless P=NP, and the current best approximation algorithm achieves the ratio of 1.5. MAX SMTI remains NP-hard even when preference lists of one side do not contain ties, and it cannot be approximated within $21/19 \ (> 1.1052)$ unless P=NP. However, even under this restriction, the best known approximation ratio is still 1.5. In this paper, we improve it to $25/17 \ (< 1.4706)$ .