Can Frost Nova with Shatter result in more than two Frost Novas?

The Frost Nova ability freezes all enemies around the Wizard for 3 seconds. Shatter reads:

A frozen enemy that is killed has a 50% chance of releasing another Frost Nova.

If a second Frost Nova occurs, does that instance also have Shatter? That is, if I kill an enemy that was (only) hit by the second Frost Nova, will I ever be able to trigger another?

Yes, the second Frost Nova appears to be a brand new Frost Nova, and it can cause a chain reaction if you're lucky

I noticed it yesterday when I was playing my Wizard with friends and we encountered a long line of enemies. I hit the front of the group, it Shattered and caused a 2nd Frost Nova, and that one Shattered and caused a third, and so forth.

I'm not actually sure how many Frost Novas occurred since there were a lot of enemies, but the final frozen enemy was quite a ways away from the initial Frost Nova, and was frozen around 10 seconds after I cast Frost Nova, which means at least 3-4 Frost Novas occurred.