We have studied the influence of the transverse size of a magnetic tunnel nanojunction on the magnitude of the magnetoresistance. During modeling, the size of the right contact was fixed, while the size of the left one gradually changed until they coincided. We found a sharp drop in the tunneling magnetoresistance (TMR) in nanocontacts with mismatched cross section. This can be explained by the peculiarities of the spatial distribution of the electron density, which is different for majority and minority-spin states. The discovered effect must be taken into account in the design of TMR-based nanodevices.