How To Make A GiF Frame Fade Into Itself?

Hello!

I need some assistance on making a GiF fade into itself. Normally, when I attempt to do this I achieve the results I'm looking for. However, as the GiF fades, it creates a white color-pop as it nears the end of the loop. For example:

Here's a random GiF with the fade transition:

As you can see, the fade transition here goes white towards the end of the GiF, which I don't have problem with. But instead having the white transition, how can I make this GiF fade into itself!? In other words, how can I make a particular frame fade into itself?

I hope my question is clear and coherent. Thank you in advance!