If an engine failure has occurred during initial climb, accomplish the appropriate
checklist after the flaps have been retracted and conditions permit.

Immediate Turn after Takeoff - One Engine Inoperative
Obstacle clearance or departure procedures may require a special engine out departure procedure. If an immediate turn is required, initiate the turn at the appropriate altitude (normally at least 400 feet AGL). Maintain V2 to V2 + 15 with takeoff flaps while maneuvering.
Note:  Limit bank angle to 15° until V2 + 15 knots. Bank angles up to 30° are permitted at V2 + 15 knots with takeoff flaps.
After completing the turn, and at or above flap retraction altitude, accelerate and retract flaps.
Copyright . The Boeing Company. See title page for details.
3.36  FCT 737 (TM) October 31, 2006
737 Flight Crew Training  Manual

Autopilot Engagement - One Engine Inoperative
737-300 - 737-500 When at a safe altitude above 1,000 feet AGL with correct rudder pedal or trim
input, the autopilot may be engaged. 737-600 - 737-900 When at a safe altitude above 400 feet AGL with correct rudder pedal or trim
input, the autopilot may be engaged.

Flap Retraction - One Engine Inoperative
The minimum altitude for flap retraction with an engine inoperative is 400 feet
AGL. During training, flap retraction is initiated at 1,000 feet AGL. At engine out flap retraction altitude, select flaps up maneuvering speed on the MCP. Engine-out acceleration and climb capability for flap retraction are functions of airplane thrust to weight ratio. The flight director commands a near level or a slight climb (0-200 fpm) flap retraction segment. Accelerate and retract flaps on the flap-speed schedule.
If the flight director is not being used at flap retraction altitude, decrease pitch attitude to maintain approximately level flight while accelerating. Retract flaps on the flap-speed schedule.
As the airplane accelerates and flaps are retracted, adjust the rudder pedal position to maintain the control wheel centered and trim to relieve rudder pedal pressure.

Flaps Up - One Engine Inoperative
After flap retraction and at flaps up maneuvering speed, select LVL CHG, set maximum continuous thrust (CON) and continue the climb to the obstacle clearance altitude.
Initiate the appropriate engine failure non-normal checklist followed by the After Takeoff checklist when the flaps are up and thrust is set. Remain at flaps up maneuvering speed until all obstructions are cleared, then select the engine-out schedule from the CDU CLB page (depending on the next course of action). Ensure the autothrottle is disconnected before reaching level off altitude. After level off, set thrust as needed.

Noise Abatement - One Engine Inoperative
When an engine failure occurs after takeoff, noise abatement is no longer a requirement.

737 Flight Crew Training  Manual

Engine Failure During an ATM Takeoff
A reduced thrust takeoff using the ATM is based on a minimum climb gradient that clears all obstacles with an engine failure after V1. If an engine failure occurs during an ATM takeoff, based on takeoff performance data, it is not necessary to increase thrust on the remaining engine. However, if more thrust is desired during an ATM takeoff, thrust on the operating engine may be increased to full takeoff thrust by manually advancing the thrust levers. The takeoff performance data provides a safe operating margin for minimum control speed on the ground (VMCG) when full takeoff thrust is set.
Advancing the operating engine to full takeoff thrust provides additional performance margin. This additional performance margin is not a requirement of the reduced thrust takeoff certification and its use is at the discretion of the flight crew.

Engine Failure During a Fixed Derate Takeoff
During a fixed derate takeoff, the takeoff performance data at low gross weights may not provide a safe operating margin for VMCG if thrust levers are advanced beyond the fixed derate limit. A thrust increase following an engine failure, especially near V1, could result in a loss of directional control and should not be accomplished unless, in the opinion of the captain, terrain contact is imminent.

Engine Failure During a Combined Takeoff
During a combined fixed derate and ATM takeoff, the takeoff performance data is based on the fixed derate takeoff thrust before the assumed temperature reduction. The takeoff performance data provides a safe operating margin for minimum control speed on the ground (VMCG) when the fixed derate takeoff thrust is selected, but not beyond the fixed derate limit. A thrust increase beyond the fixed derate limit following an engine failure, especially near V1, could result in a loss of directional control and should not be accomplished unless, in the opinion of the captain, terrain contact is imminent.
　
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