Change Custom Timer Job Schedule

Hello:

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?

I changed the schedule in the feature activation code, redeployed solution and re-activate the feature? Do I need to uninstall the feature and try activating it? Making changes to existing custom timer job seems to be so confusing.

Thanks!