Transparent pulses are defined by the property of having no net effect on stationary spins, while selectively nutating and dephasing flowing spins. They are derived from the inverse scattering transform, a nonlinear extension of the inverse Fourier transform. They can be used as presaturation pulses to suppress selectively the signal from flowing spins. Their intended imaging application is suppression of blood flow artifacts arising from the heart and major vessels. Diastolic images of these areas have significant artifacts that hinder accurate delineation of vessel and chamber boundaries. Transparent pulses significantly improve delineation of these boundaries and therefore could be used to improve the accuracy and precision of cross-sectional area measurements. In this paper, the analytic theory, numerical optimization, and performance characteristics are described. Experimental evidence of flow signal suppression is provided in diastolic imaging of the heart in normal subjects. The long duration and power requirements of the present generation of transparent pulses currently limits their general clinical use.