Abstract: Based on the properties of the quadratic variation of local square integrable strong martingales, the stochastic integral of predictable processes with respect to local square integrable strong martingales is defined. Some important results that this stochastic integral is still local square in tegrable strong martingale are obtained. These results contain and extend some results which have been proved by Cairoli and Walsh.

Key words: stopping line, local square strong martingale, stoch astic integral