  We construct pure two-bubbles for the energy-critical focusing nonlinear
Schr\"odinger equation in space dimension $N \geq 7$. The constructed solution
is global in (at least) one time direction and approaches a superposition of
two stationary states both centered at the origin, with the ratio of their
length scales converging to $0$. One of the bubbles develops at scale $1$,
whereas the length scale of the other converges to $0$ at rate
$|t|^{-\frac{2}{N-6}}$. The phases of the two bubbles form the right angle.
