United Airlines is anticipating that Boeing’s (BA) grounded 787 Dreamliner will be ready for a flight by the end of next month, according to the carrier’s flight schedule.

A 787 flight from Houston to Denver is penciled in for May 31, a show of optimism from United Airlines that the jet will be cleared for takeoff by the Federal Aviation Administration.

Boeing conducted on Friday its final certification test flight for a redesigned Dreamliner battery system. The plane maker is waiting for FAA approval before sending out battery repair kits to airlines.

“We are in the process of formulating our domestic flying plans and will be making additional schedule changes as we gain visibility into the timeline for certification and modification work,” United Airlines said in a statement.  “We are currently planning to begin international flying on the Denver-Narita route on June 10, and in the period preceding that, we will conduct domestic flying with the 787.”

United Continental Holdings (UAL) shares closed Monday up 2.6% at $30.05. Boeing also ended the day strong, trading 58 cents higher at $86.75.

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