Problem: Draw Framebuffer on Framebuffer

I am new to OpenGL but I have some knowledge already about it.
My problem:
I created two FBOs with the same size. The first FBO was rendered to the second FBO and the second FBO was rendered to the screen. It seemed like there was no problem but when I changed the size of the first FBO to half size the drawn content on the first FBO was scaled by the value 0.5.

To better understand this I have some screenshots:
Without problems:

With scaling problem:

red: second FBO
gray: first FBO
black: background