Gusty weather and heavy rain is predicted, although the winds will be less severe than yesterday, forecasters said.
Stormy weather disrupted road, rail and ferry travel and left hundreds of homes without power.
The height of the storm was felt late afternoon and early evening, with a gust of 72mph recorded in Glasgow and an 85mph gust in Glen Ogle in Stirlingshire.
Edinburgh Castle was evacuated when winds reached 75mph.
Fallen trees yesterday forced the cancellation of a number of rail services. Trains from Glasgow to Largs and Ardrossan had to stop at Kilwinning while buses replaced trains after a signal failure at Helensburgh in Argyll and Bute.
Fallen trees also brought trains to a halt at Gourock, Falkirk and Bishopton.
Forecasters said that the wind would ease slightly today, but travellers were still being warned of possible disruptions on the roads, rail and ferries.
ScotRail today advised customers to check their website before travel.
A statement on their website said: "We are constantly monitoring the situation and it is our intention to run a full service on 13 September, subject to no deterioration in weather conditions."
Paul Mott, a forecaster with MeteoGroup, the weather division of the Press Association, said: "It will not be as windy as yesterday but there will be strong winds over central and southern Scotland with gusts of up to 55mph.
"It will be another gusty day. At the moment the winds are starting to ease down but they will start to pick up throughout the morning."
Drivers were also warned to take extra care on the roads.
In Ayrshire, the A70 Muirkirk Road in Cumnock is closed in both directions near the Glenmuir Road junction, because of a fallen tree.
The Erskine Bridge is closed to high sided vehicles between the M898 J1 junction and the A814 junction, because of strong winds.
Early morning ferry services faced disruption with P&O Fastcraft sailings cancelled between Cairnryan and Larne.
Calmac were warning of possible delays between Rothesay and Wemyss Bay. The operator also cancelled the 7am service between Ardrossan and Brodick.
At the airports, FlyBE's early morning flight from Islay to Glasgow was cancelled.
In Ayrshire and Dumfries around 200 Scottish Power customers were left without electricity yesterday.
The company said engineers were working to reconnect them last night.
ScotRail said services were disrupted by the high winds with routes between Glasgow Central and Largs/Ardrossan, Glasgow and Helensburgh Central affected. There was also disruption at Gourock, Falkirk Grahamston and Bishopton due to fallen trees yesterday.
Clyde Coastguard received several call-outs yesterday with boats adrift from their moorings along the west coast, but there was no reports of any injuries.
In Fairlie, in Ayrshire, a 200 tonne barge broke free of its moorings and ended up on the beach.
Witnesses said at one point it looked like the barge may have ended up on the main street.
Firefighters were yesterday called out to deal with a dangerous structure at Burnbank Road in Hamilton, Lanarkshire.
A billboard had become loose and it was feared it may have fallen or damaged the building it was attached to.
There was also a concern for parked cars and passers by being struck if the billboard had come loose.
A high reach appliance was drafted in from Motherwell along with a heavy rescue vehicle from Easterhouse and made the billboard safe.
Transport Minister Keith Brown today advised people to check latest travel information before they set off.
He said: "More strong winds and heavy rain is forecast making travel conditions difficult in particular the impact high winds could have on traffic over our bridges.
"While we are all working hard to keep Scotland moving, it's important the travelling public are prepared."