A stirrup for horse-riding comprising a tread , a first end of which is connected by a first side branch to an upper portion adapted to receive a stirrup leather, the stirrup comprising a second side branch movable between: - a position for use, in which said second side branch connects a second end portion of said tread to said upper portion , - an open position, in which said second side branch is distanced from said second end portion of said tread , wherein - in the said position for use the second side branch is rendered integral with the second end portion of the tread by magnetic attraction. characterized in that : - said second side branch is connected to said upper portion by a swivel linkage, - this swivel linkage allows pivoting of the outer side branch 2 relative to upper portion in any direction; - said swivel linkage is constituted by an elastic cord urging a surface of said upper portion and a surface of said second side branch towards each other, - said surface of said upper portion and said surface of said second side branch have complementary shapes adapted to maintain said second side branch in said position for use, when said surfaces are in contact, - said surface of said upper portion and said surface of said second side branch have complementary shapes adapted to maintain said second side branch in said position for use, when said surfaces are in contact, - said surface of said second side branch has a centering stud , and said surface of said upper portion has a recess of complementary shape to that of said centering stud , said centering stud being introduced, in said position for use, into said recess , - said centering stud has a triangular cross-section. - a position for use, in which said second side branch connects a second end portion of said tread to said upper portion , - an open position, in which said second side branch is distanced from said second end portion of said tread , wherein - in the said position for use the second side branch is rendered integral with the second end portion of the tread by magnetic attraction. characterized in that : - said second side branch is connected to said upper portion by a swivel linkage, - this swivel linkage allows pivoting of the outer side branch 2 relative to upper portion in any direction; - said swivel linkage is constituted by an elastic cord urging a surface of said upper portion and a surface of said second side branch towards each other, - said surface of said upper portion and said surface of said second side branch have complementary shapes adapted to maintain said second side branch in said position for use, when said surfaces are in contact, - said surface of said upper portion and said surface of said second side branch have complementary shapes adapted to maintain said second side branch in said position for use, when said surfaces are in contact, - said surface of said second side branch has a centering stud , and said surface of said upper portion has a recess of complementary shape to that of said centering stud , said centering stud being introduced, in said position for use, into said recess , - said centering stud has a triangular cross-section. <EOS>