We investigate the transport properties of a pair of Majorana bound states in a T-shaped junction, where two normal leads are coupled with an identical Majorana bound state. Both the scattering matrix and the recursive Green function method show that the peak value of the differential conductance (G_peak) in units of e²/h and the shot noise Fano factor in the zero bias limit (F₀), which are measured at the same lead and zero temperature, satisfy a linear relation as F₀=1+G_peak/2, independent of the magnitude or symmetry of the coupling strengths to the leads. Therefore, combined measurements of the differential conductance and shot noise in the T-shaped geometry can serve as a characteristic signature in probing Majorana bound states.