We investigate the mixed-spin (spin-1/2 and spin-1) antiferromagnetic Ising
model in two dimensions through a real-space renormalization group transfo
rmation. The model includes nearest and next-nearest neighbor interactions
and is suitable to describe ferrimagnetic ordering. We present the finite-t
emperature phase diagram of the model. The presence of the second-neighbor
bonds enlarge the ferrimagnetic phase. Our results do not indicate the exis
tence of a tricritical point, contrary to previous effective-field calculat
ions.