At 0954 GMT commercial banks in Kampala quoted the currency of east Africa's third largest economy at 2,465/2,475, unchanged from Thursday's close.
"Over the last two weeks we've seen overnight and one-week rates come down significantly and this now makes it much cheaper to fund dollar positions," said David Bagambe, trader at Diamond Trust Bank.
"Next week stability will hold but a likely surge in dollar purchases in the interbank market might put moderate pressure on the shilling."
He said overnight rates stood at between 12-15 percent, after coming down from around 21 percent two weeks ago.
Weak greenback demand has kept the shilling stable against the dollar for several weeks now despite two straight months of key rate cuts by the central bank.
The Bank of Uganda's benchmark lending rate was cut this month to 19 percent from June's 20 percent but analysts say it will take time before the policy easing soaks through the economy and spurs a surge in dollar demand.
A Bank of Africa market brief suggested the shilling was likely to remain stable but biased toward weakening.
"Market players seem to be running with averagely square positions as the long term outlook poses a threat to the local unit," the brief said.