An ultrasonic horn for use with an ultrasonic surgical handpiece including a resonator comprises a linear cutting blade at the distal end of a horn body. The linear cutting blade includes adjacent side-by-side rows of teeth each of which includes a land through which ultrasonic energy is propagated outwardly from the distal end. The lands of the rows of teeth are angled so that the propagated ultrasonic energy of one plurality of lands intersects the propagated ultrasonic energy from the other row of lands. Shear stress fields are developed at the intersections of the ultrasonic energy that will perform the cutting function on target tissue. An irrigation arrangement is also disclosed.