The baryon decay modes of B, (B) over bar -> N1N2(f), N1N2(f) provide a frame work to test CP-invariance in baryon sector. It is shown that in the rest frame of B, N-1 and (N) over bar (2) come out with longitudinal polarization lambda(1)=lambda(2)=+/- 1 with decay width Gamma(f)=Gamma(++)(f)+Gamma(--)(f) and the asymmetry parameter alpha(f)=Delta Gamma(f)=(Gamma(++)(f)-Gamma(--)(f))/Gamma(f). It is shown that CP invariance prediction alpha(f)=-(alpha) over bar (f) can be tested in these decay modes; especially in the time-dependent decays of B-q(0)-(B) over bar (0)(q) complex. Apart from this, it is shown that decay modes B((B) over bar)-> N-1(N) over bar (2)((B) over bar N-1(2)) and subsequent nonleptonic decays of N-2, (B) over bar (2) or (N-1,(B) over bar (1)) into hyperon (antihyperon) also provide a frame work to study CP-odd observables in hyperon decays.