Can you move the Hunter’s Mark spell on the same turn that the affected creature dies?

The hunter’s mark (and also hex) spell contains the following text:

[…] If the target drops to 0 hit points before this spell ends, you can use a bonus action on a subsequent turn of yours to mark a new creature […]

Does this passage prevent the following scenario:

  1. Cast hunter’s mark on somebody
  2. Your turn ends
  3. Another one of your turn’s begins
  4. You kill the targeted creature
  5. You place hunter’s mark onto a new target as a bonus action

Is step 5 in the above prevented from working due to the wording of the hunter’s mark spell? It seems like it would be to me, but perhaps I’ve missed something somewhere.