The transcritical blowout bifurcation of a quasiperiodic torus on an invariant subspace is studied in this paper. We found that the strange nonchaotic attractor (SNA) beyond the blowout bifurcation is only a weak attractor in the sense of Milnor. This is different from the popularly studied case where the Milnor attractor is a chaotic one with a riddled basin of attraction. Characters of this Milnor SNA and the influence of a random noise are studied.