Abstract: Disclosed is a method for the heat treatment of at least one bar made from titanium aluminide alloy for manufacturing at least one low-pressure turbine blade for a turbomachine, comprising hot isostatic pressing of the bar, characterised in that the hot isostatic pressing (121) is followed, after a temperature transition phase, by a step of heat treatment (122) of the bar at a temperature in the immediate vicinity of the eutectoid temperature of the alloy, the temperature being suitable for the formation of an alloy microstructure with a volume fraction of at least 90% single-phase grains ? and a volume fraction of at most 10% of lamellar grains ?+?, the step being followed by a controlled cooling step (123).