A method for making a bolometric detector comprising at least the implementation of the following steps of: - making a stack of layers (29, 30, 32, 34) over an electrical interconnect level of an electronic read-out circuit of the detector, the stack comprising at least one sacrificial layer arranged between a support layer and a first etch stop layer, the first etch stop layer being arranged between the sacrificial layer and said electrical interconnect level, and the sacrificial layer comprising at least one mineral material capable of being etched selectively with respect to the support layer and the first etch stop layer; - making at least one electrically-conductive via crossing at least the stack of layers (29, 30, 32, 34) such that at least one electrically-conductive material of the via is in contact with at least one electrically-conductive portion of said electrical interconnect level connected to the electronic read-out circuit; - depositing at least one electrically-conductive layer over the support layer and the via; - etching the electrically-conductive layer and the support layer, forming a bolometer membrane electrically connected to the via by at least one remaining portion of the electrically-conductive layer that covers at least one upper portion of the via; - eliminating the sacrificial layer by chemical etching to which the first etch stop layer and the support layer are resistant, and such that the membrane is suspended by means of the via; wherein the stack of layers (29, 30, 32, 34) further includes a second etch stop layer such that the support layer is arranged between the second etch stop layer and the sacrificial layer, the method further including, between making the via and depositing the electrically-conductive layer, the implementation of the following steps of: - removing an electrically-conductive material layer formed over the second etch stop layer during making of the via, then - eliminating the second etch stop layer, and wherein the electrically-conductive layer is deposited such that the remaining portion of the electrically-conductive layer also covers lateral sidewalls of the upper portion of the via uncovered by the elimination of the second etch stop layer. - making a stack of layers (29, 30, 32, 34) over an electrical interconnect level of an electronic read-out circuit of the detector, the stack comprising at least one sacrificial layer arranged between a support layer and a first etch stop layer, the first etch stop layer being arranged between the sacrificial layer and said electrical interconnect level, and the sacrificial layer comprising at least one mineral material capable of being etched selectively with respect to the support layer and the first etch stop layer; - making at least one electrically-conductive via crossing at least the stack of layers (29, 30, 32, 34) such that at least one electrically-conductive material of the via is in contact with at least one electrically-conductive portion of said electrical interconnect level connected to the electronic read-out circuit; - depositing at least one electrically-conductive layer over the support layer and the via; - etching the electrically-conductive layer and the support layer, forming a bolometer membrane electrically connected to the via by at least one remaining portion of the electrically-conductive layer that covers at least one upper portion of the via; - eliminating the sacrificial layer by chemical etching to which the first etch stop layer and the support layer are resistant, and such that the membrane is suspended by means of the via; wherein the stack of layers (29, 30, 32, 34) further includes a second etch stop layer such that the support layer is arranged between the second etch stop layer and the sacrificial layer, the method further including, between making the via and depositing the electrically-conductive layer, the implementation of the following steps of: - removing an electrically-conductive material layer formed over the second etch stop layer during making of the via, then - eliminating the second etch stop layer, - removing an electrically-conductive material layer formed over the second etch stop layer during making of the via, then - eliminating the second etch stop layer, and wherein the electrically-conductive layer is deposited such that the remaining portion of the electrically-conductive layer also covers lateral sidewalls of the upper portion of the via uncovered by the elimination of the second etch stop layer.