NAIROBI, July 4 (Reuters) - The Kenyan shilling firmed against the dollar on Monday as commercial banks kept selling dollars in the wake of the central bank's increase in the overnight lending rate. But traders said they were watching for corporates to take advantage of the shilling's gains and begin buying back the greenback. The local currency gained for four straight days last week. The Central Bank of Kenya set an overnight discount rate of 8.0 percent on Wednesday, and said the rate will be posted on its website everyday at 0600 GMT, in a bid to tame a volatile currency and rising inflation. The discount rate was unchanged at 8.0 percent on Monday. At 0613 GMT, commercial banks quoted the shilling at 88.40/60 against the dollar, stronger than Friday's close of 88.70/80. "The shilling is still supported by high rates, but we would want to see if there would be some pent up demand from corporate clients who have been staying away." said Dickson Magecha, a trader at Standard Chartered Bank. Traders said they expected the shilling to trade in the 88.00-89.00 range on Monday. They said they expected the central bank to stay out of the foreign exchange market for now as the market reacts to the rate rise. The bank's attempts to mop up shillings from the market through repurchase agreements failed to attract any bids from banks for the 14th straight session on Friday

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