* HSI +0.1 pct, H-shares flat, CSI300 +0.5 pct
* China software firms jump, leading tech-sector gains
* Airlines rise lifted by stronger yuan
* Hainan Rubber at 6-mth high on agricultural reform optimism (Updates to midday)
By Grace Li
HONG KONG, Sept 11 (Reuters) - China shares regained momentum on Thursday and hit fresh multi-month highs, lifting a sluggish Hong Kong market, supported by recovering banks and brokerage companies.
A focus for the market was China's August inflation data which showed consumer inflation cooled more than expected. While it provided further evidence of economic slowdown, hopes were raised that policymakers would have room for more stimulus measures if needed.
By midday, the Hang Seng Index inched up 0.1 percent to 24,732.87 points following four days of losses. The China Enterprises Index of the top Chinese listings in Hong Kong was flat.
The CSI300 of the leading Shanghai and Shenzhen A-share listings was up 0.5 percent, earlier testing a 9-month high. The Shanghai Composite Index also added 0.5 percent at 2,329.07 points, after hitting its highest since March 2013 in late morning trade.
The onshore markets slipped on Wednesday after Premier Li Keqiang signalled weak credit data for August.
"The impact was limited. The overall sentiment remains optimistic," said Zhang Qi, a Shanghai-based analyst with Haitong Securities.
"Investors are expecting more funds flowing in with the Shanghai-Hong Kong trading link approaching. And state media including Xinhua News Agency and People's Daily have said recently the equity market should play a positive role in the economy, so there's policy support," Zhang added.
CITIC Securities and Haitong Securities , major contributors to CSI300 gains, climbed 2.0 and 1.8 percent, respectively.
Technology counters outperformed on Thursday, tracking a rise in the the Nasdaq Composite overnight. Neusoft Corp and Beijing Join-Cheer Software soared the maximum allowed 10 percent limit.
Hainan Rubber Industry Group also jumped by the daily limit of 10 percent to a six-month high on hopes that the land-rich company would benefit from accelerated land transfers brought about by upcoming agricultural reforms.
Chinese airlines were broadly firmer on expectations they would benefit from a stronger currency. China East Airlines rose 1.0 percent in Shanghai and China Southern Airlines advanced 1.1 percent in Hong Kong.
China's yuan strengthened to a six-month high against the dollar earlier this week after the central bank set a sharply stronger midpoint even amid worries that the economy is slowing.
In Hong Kong, profit-taking continued to hurt major energy companies, restricting index gains. CNOOC slid 1.0 percent and PetroChina 0.6 percent. (Editing by Jacqueline Wong)