Assembly comprising: a building with an external wall; an inlet/outlet pipe system for supplying air to a combustion plant set up inside the building and for discharging flue gases coming from said combustion plant respectively; in which the inlet/outlet pipe system at one end projects through the external wall to the outside, and on that one end comprises an inlet/outlet mouthpiece situated substantially on the outside of the external wall; in which the inlet/outlet mouthpiece comprises: a horizontally extending inlet pipe part with an inflow end for allowing air to flow in from the environment; a horizontally extending outlet pipe part with an outflow part for allowing flue gases to flow out to the environment; in which the outlet pipe part extends through and substantially parallel to the inlet pipe part and projects from the inflow end of the inlet pipe part in such a way that the outflow part of the outlet pipe part lies outside the inlet pipe part; and in which the bottom (17, 20) of the outlet pipe part extends upwards at a slope (β), characterized in that the outflow part comprises an internal diameter which diverges in the longitudinal direction of the outlet pipe part to reduce the velocity of flue gases flowing through the outflow part; in which the free end of the outflow part is provided with a cap extending transversely to the longitudinal direction of the outflow part; and in which the outflow part has an underside, an upper side and sides extending between the underside and upper side, the underside and upper side of the outflow part being closed, and the sides being provided with windows for allowing flue gases to flow out laterally. a building with an external wall; an inlet/outlet pipe system for supplying air to a combustion plant set up inside the building and for discharging flue gases coming from said combustion plant respectively; in which the inlet/outlet pipe system at one end projects through the external wall to the outside, and on that one end comprises an inlet/outlet mouthpiece situated substantially on the outside of the external wall; in which the inlet/outlet mouthpiece comprises: a horizontally extending inlet pipe part with an inflow end for allowing air to flow in from the environment; a horizontally extending outlet pipe part with an outflow part for allowing flue gases to flow out to the environment; in which the outlet pipe part extends through and substantially parallel to the inlet pipe part and projects from the inflow end of the inlet pipe part in such a way that the outflow part of the outlet pipe part lies outside the inlet pipe part; and in which the bottom (17, 20) of the outlet pipe part extends upwards at a slope (β), characterized in that the outflow part comprises an internal diameter which diverges in the longitudinal direction of the outlet pipe part to reduce the velocity of flue gases flowing through the outflow part; in which the free end of the outflow part is provided with a cap extending transversely to the longitudinal direction of the outflow part; and in which the outflow part has an underside, an upper side and sides extending between the underside and upper side, the underside and upper side of the outflow part being closed, and the sides being provided with windows for allowing flue gases to flow out laterally. a horizontally extending inlet pipe part with an inflow end for allowing air to flow in from the environment; a horizontally extending outlet pipe part with an outflow part for allowing flue gases to flow out to the environment; in which the outlet pipe part extends through and substantially parallel to the inlet pipe part and projects from the inflow end of the inlet pipe part in such a way that the outflow part of the outlet pipe part lies outside the inlet pipe part; and in which the bottom (17, 20) of the outlet pipe part extends upwards at a slope (β), characterized in that the outflow part comprises an internal diameter which diverges in the longitudinal direction of the outlet pipe part to reduce the velocity of flue gases flowing through the outflow part; in which the free end of the outflow part is provided with a cap extending transversely to the longitudinal direction of the outflow part; and in which the outflow part has an underside, an upper side and sides extending between the underside and upper side, the underside and upper side of the outflow part being closed, and the sides being provided with windows for allowing flue gases to flow out laterally.