Residual Sounds When Playing Scales

I've just started working on scales- the Am pentatonic is my first one. My question is, when I play tyhe next note on the scale and lift my finger off the previous note, I still get the sound of the previous note while I am forming the new note, so it's not clean. Is there something I am doing wrong? What I think I should be playing is discrete notes without the residual sound of the former note still sounding when I play the new note.