You can try instead of moving the finger down and then lift it, to somehow "pick" the next note. By this instead of making two movements do a diagonal one with which you are giving strength to the next note, but not changing the initial pitch. To see an example try picking with your pick hand's middle finger an open string. Notice that if you move the string and then make it sound, it won't sound to good, instead if you do the diagonal movement, it'll sound better.