A turbine ring assembly extending around an axis, including 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 including a base from which an upstream tab and a downstream tab extend radially outward, spaced axially from one another, wherein the assembly also includes a cross-member mechanically connected to the ring support and including 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 through the upstream latching tab and the downstream latching tab of the ring sector and the ring support to hold the ring sector and the ring support secured to one another.