Systematic theoretical study on possible antimagnetic rotation in <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mmultiscripts><mml:mi>Pd</mml:mi><mml:mprescripts/><mml:none/><mml:mrow><mml:mn>103</mml:mn><mml:mo>,</mml:mo><mml:mn>105<

The possible antimagnetic rotation (AMR) of the four negative-parity yrast bands with four ${g}_{9/2}$ valence proton holes in the isotopes $^{103,105,107,109}\mathrm{Pd}$ is systematically investigated by using the cranked shell model with pairing correlations taken into account by a particle-number-conserving treatment. The calculated values of $B(E2$) after backbending agree well with the available experimental data, which display decreasing tendency with the rotational frequency. The two-shears-like mechanism is clearly exhibited in the case of four valence proton holes. Accordingly, we verify the AMR properties of the $^{103}\mathrm{Pd}$ negative-parity yrast band recognized previously in the literature, and suggest the negative-parity yrast bands of $^{105,107,109}\mathrm{Pd}$ as three new candidates for an AMR band, thereby extending the Pd isotope chain with AMR by four mass units towards the neutron-rich side.