We investigate the effects of Co doping and high pressure on 122-type La0.4Na0.6Fe2As2 by electrical resistivity measurement. It is found that the antiferromagnetic (AFM) transition in La0.4Na0.6Fe2As2 is gradually suppressed with Co doping or application of pressure, whereas no intrinsic bulk superconductivity (SC) emerges. This behavior is in stark contrast to other iron-based superconductors, in which SC generally arises after the suppression of AFM order by Co doping or pressure.