The vortex identification method based on normalized angular momentum functions is revisited. In the original method, the function locating the vortex center is not a Galilean invariant. In order to overcome this drawback, the function was modified by adding the convective velocity term determined as the average velocity over the vortex core. This method was then verified through numerical simulations of the Lamb-Oseen vortex in the freestream. Applications of this method to velocity fields obtained by Particle Image Velocimetry (PIV) through wind tunnel experiments on a wing and a propeller blade are discussed. This modified method with enhanced Galilean invariance showed an overall better accuracy and robustness of vortex detection.