According to my understanding:

 - two orthogonal forces aren't related and two orthogonal vectors don't affect each other
 - the force of static friction $F_s$ depends on the normal force $F_n$, so $$F_s = \mu_s F_n$$ ($\mu_s$ being the static friction coefficient).

If these two are correct, how can the force of static friction, determined by a force normal to the surface, be directed tangential to the surface and orthogonal to the normal force?