The invention relates to a receiver for a near-field chip-to-chip multichannel transmission system such as the capacitive or inductive links used for vertical signal transmission between the stacked chips of a system-in-package. A receiver for near-field chip-to-chip multichannel transmission providing 4 transmission channels for digital transmission between two monolithic integrated circuits comprises 4 coupling devices (211) (212) (213) (214), each of said coupling devices being a planar winding sensitive to magnetic field variations. A multiple-input-port and multiple-output-port amplifier (23) has 4 input ports, each of said input ports being connected to one and only one of said coupling devices (211) (212) (213) (214). The receiver also comprises 4 recovery circuits (281) (282) (283) (284), each of said recovery circuits having an input port connected to one of the output ports of the multiple-input-port and multiple-output-port amplifier (23), each of said recovery circuits having an output terminal connected to the user (29). The receiver of the invention reduces crosstalk between the transmission channels.