Abstract: The present invention provides a method of laser machining a cooling hole in a hollow gas turbine component, the cooling hole including a circular cross section metering hole and a diffuser with an opening which extends from a shape locus in the metering hole to a trapezoidal cross section opening by firing a series of laser pulses at an acute angle at the outer surface of the component toward the shape locus to create the diffuser opening, with the laser pulses penetrating the component outer surface up to but not substantially beyond the shape locus, then firing the laser through the shape locus and the inner surface of the component to create the metering hole having a circular cross section. Alternatively, the initial laser pulses are fired to create the central portion of the diffuser opening, then firing the laser to create the metering hole, followed by firing the laser along the peripheral portion of the diffuser opening.