Repeated sprite, how do I render the outside of the sprite borders?

I’ve made this background using a tiled image with a repeatable sprite:
bg
If you look closely though, the squares are being cut off at the sprite borders.

Here’s the sprite sheet for the animation:


The sprite borders are where I want the sprite to be repeated, but that causes the outside of the border to be cut off.

Does anyone have a different approach or knows how to make the sprites not cut off?
It has to be as efficient as this though, 200+ squares would half the FPS.