Stacking machine for stacking flat items comprising an infeed end (4, 5) for flat items and a discharge end for bundles (33A, 33B, 33C, 33D) of flat items; and stacking means (18, 19, 24, 24') in which flat items successively received from the infeed end (4, 5) are stacked to form successive bundles (33A, 33B, 33C, 33D) from stacks of stacked flat items; the stacking machine further comprising: a first stacking table and a second stacking table arranged in respective horizontal planes vertically parallel to one another; first displacement means susceptible to displacing the first stacking table in a longitudinal plane and in a vertical plane at least between a stacking position in which the first stacking table receives flat items to successively form first bundles (33B, 33D) and an unloading position in which the bundles (33B, 33D) are successively transferred from the first stacking table to unloading means; second displacement means susceptible to displacing the second stacking table in said longitudinal plane and in said vertical plane at least between said stacking position in which the second stacking table receives flat items to successively form second bundles (33A, 33C) when the first stacking table is not in said stacking position, and said unloading position in which the bundles (33A, 33C) are successively transferred from the second stacking table to said unloading means; characterized in that the stacking machine further comprises: coupling means (41, 42) to alternatively couple the first stacking table and the second stacking table to the unloading means for collecting successive bundles (33A, 33B, 33C, 33D) coming from the stacking tables (18, 19) when said stacking tables (18, 19) are in the stacking position with the already finished bundle and which automatically decouple when the stacking tables (18, 19) are in a standby position. a first stacking table and a second stacking table arranged in respective horizontal planes vertically parallel to one another; first displacement means susceptible to displacing the first stacking table in a longitudinal plane and in a vertical plane at least between a stacking position in which the first stacking table receives flat items to successively form first bundles (33B, 33D) and an unloading position in which the bundles (33B, 33D) are successively transferred from the first stacking table to unloading means; second displacement means susceptible to displacing the second stacking table in said longitudinal plane and in said vertical plane at least between said stacking position in which the second stacking table receives flat items to successively form second bundles (33A, 33C) when the first stacking table is not in said stacking position, and said unloading position in which the bundles (33A, 33C) are successively transferred from the second stacking table to said unloading means; characterized in that the stacking machine further comprises: coupling means (41, 42) to alternatively couple the first stacking table and the second stacking table to the unloading means for collecting successive bundles (33A, 33B, 33C, 33D) coming from the stacking tables (18, 19) when said stacking tables (18, 19) are in the stacking position with the already finished bundle and which automatically decouple when the stacking tables (18, 19) are in a standby position. coupling means (41, 42) to alternatively couple the first stacking table and the second stacking table to the unloading means for collecting successive bundles (33A, 33B, 33C, 33D) coming from the stacking tables (18, 19) when said stacking tables (18, 19) are in the stacking position with the already finished bundle and which automatically decouple when the stacking tables (18, 19) are in a standby position.