A turbine ring assembly extending around an axis (X-X), comprising a plurality of ring sectors made of ceramic matrix composite material, forming a turbine ring and a ring support structure held by a turbine casing, each ring sector comprising a base from which an upstream latching tab and a downstream latching tab, spaced axially away from one another, extend radially outward, the assembly additionally comprising: - a cross-member mechanically connected to the ring support structure and comprising a first radial flange bearing against the upstream latching tabs of the ring sectors, and - for each ring sector, at least two transverse pins and a radial spring, each transverse pin passing though the upstream latching tab and the downstream latching tab of the ring sector and the ring support structure to hold the ring sector and the ring support structure secured to one another, the ring support structure also comprising a second radial flange bearing against the downstream latching tabs of the ring sectors, the upstream latching tab and the downstream latching tab of each ring sector being arranged axially between the first radial flange and the second radial flange, characterized in that the assembly further comprises a radial spring being held bearing, in a radial direction (D R) orthogonal to the axial direction (X-X), against the ring sector on the one hand and against the ring support structure on the other hand to hold the ring sectors arranged at the same radial position and in that said first radial flange comprises a first portion and a second portion radially inside the first portion, the second portion including a first tab and a second tab axially distant from one another and both secured to the first portion, the first tab being axially upstream of the second tab, and the second tab bearing against the upstream latching tab. the assembly additionally comprising: - a cross-member mechanically connected to the ring support structure and comprising a first radial flange bearing against the upstream latching tabs of the ring sectors, and - for each ring sector, at least two transverse pins and a radial spring, each transverse pin passing though the upstream latching tab and the downstream latching tab of the ring sector and the ring support structure to hold the ring sector and the ring support structure secured to one another, - a cross-member mechanically connected to the ring support structure and comprising a first radial flange bearing against the upstream latching tabs of the ring sectors, and - for each ring sector, at least two transverse pins and a radial spring, each transverse pin passing though the upstream latching tab and the downstream latching tab of the ring sector and the ring support structure to hold the ring sector and the ring support structure secured to one another, the ring support structure also comprising a second radial flange bearing against the downstream latching tabs of the ring sectors, the upstream latching tab and the downstream latching tab of each ring sector being arranged axially between the first radial flange and the second radial flange, characterized in that the assembly further comprises a radial spring being held bearing, in a radial direction (D R) orthogonal to the axial direction (X-X), against the ring sector on the one hand and against the ring support structure on the other hand to hold the ring sectors arranged at the same radial position and in that said first radial flange comprises a first portion and a second portion radially inside the first portion, the second portion including a first tab and a second tab axially distant from one another and both secured to the first portion, the first tab being axially upstream of the second tab, and the second tab bearing against the upstream latching tab.