To prevent the generation of a torque sink, while shortening a torque phase time, in an automatic transmission for changing the speed by the shift of a friction engaging element.

When the tightening pressure of the friction engaging element of a release side is lowered gradually, while the tightening pressure of the friction engaging element of a tightening side is increased geadually, the existence/absence of a slip in the friction engaging element of the release side is detected based on a turbine rotation speed or gear ratio. When the generation of the slip is detected, the raising speed of the tightening pressure of the friction engaging element of the tightening side is changed largely than the value upto now.