This exercise is from the Core Skills section on developing Speed Techniques. As usual, check out the normal speed audio first.

So far we've been building up alternate picking skills just along 1 string. It's time to work at picking across strings. This is a warm up exercise used by the likes of Steve Vai, and it's very effective for helping you get tight and consistent with alternate picking across strings.

The exercise is simple, but hard to do fast. Use constant down / up strokes as you progress across each string. Just play 4 notes per string, all starting at fret 5. Except on the high E string, start descending downwards through notes on the fretboard instead of ascending.

If you do it right, you will start with a downstroke every time you switch to a new string whilst ascending through the notes. On descending, you will start each new string with an upstroke.

Go as slow as you need until you get consistent timing with each pick stroke. Eliminate any 'gaps' as you switch between strings. Each note should last for the same duration of time. Practice at that speed until everything is tight and flows properly. Only then should you work at ramping up the speed.