NEW YORK (MarketWatch) -- Southwest Airlines Co. said Thursday that it had to repair four of the 38 planes grounded earlier this week after an internal investigation revealed the planes hadn't been properly inspected.

The Dallas-based carrier said that repairs to the Boeing Co. BA, -1.49% 737 aircraft were being carried out, with 34 other planes returning to service. Altogether, Southwest reinspected 44 aircraft, including six already grounded, for possible fuselage cracks.

Southwest LUV, -1.64% is continuing with its investigation, but as for now no other planes have been grounded, a spokeswoman said. The carrier operates 520 aircraft in total, all of them Boeing 737s.

The maintenance review, launched Tuesday, followed the Federal Aviation Administration's announcement last week of a proposed $10.2 million fine against the company after finding six of 45 inspected aircraft showed fatigue cracks.

A review of maintenance records reveled procedural problems, and Southwest grounded the 38 craft, or 7.3% of its fleet, for reinspection -- canceling about 4% of its flights.

But it was the right move because the groundings showed how serious Southwest's management takes safety, according to Daniel Ortwerth, an industrial analyst with Edward Jones, who said that he expects a minimum impact to the carrier's top line due to the cancellations.

Ortwerth has a hold rating on the stock. See full interview.

Southwest said Wednesday night that it worked with its ground crews to clarify inspection procedures, particularly for two, smaller areas on the aircraft that were undisclosed.

Inspections can be done visually or with an electronic device that can uncover fuselage cracks unseen by the naked eye, said Chris Mainz, a spokesman for the airline. He declined to comment on whether the crews may not have chosen the right procedure for inspecting those areas of the 737.

Southwest shares rose 1.8% Thursday to close at $11.70.