In a magnetic resonance angiography method with flow-compensated and flow-sensitive imaging and a magnetic resonance apparatus for implementing such a method, a first MR data set of the examination region is acquired with an imaging sequence in which vessels in the examination region are shown with high signal intensity, a second MR data set of the examination region with an imaging sequence in which the vessels in the examination region are shown with low signal intensity, and the angiographic magnetic resonance image is calculated in a processor by taking the difference of the first and second data set. The first data set is acquired with an imaging sequence with reduced flow sensitivity and the second data set is acquired with an imaging sequence with an increased flow sensitivity compared to the initial imaging sequence.