Change Timer Job Schedule

I deployed a custom timer job via a feature to run weekly on Sundays at midnight. I would like to change the schedule to Sundays at noon. To make this change, I went into central administration and changed the job schedule via. job definitions page.

To my surprise, after I made this change, the timer job seems to be running twice once at midnight and another time at noon. It's as if there are two timer job instances running on two schedules i.e., old timer job instance was not deleted or purged. Why is that?

What is the correct way to change the schedule of a timer job? Do I need to make the change in the feature activation code and re-activate it?

Thanks!