LetGL(n,R) be the general linear group ofn × nreal matrices. Definitions ofGL(n,R)‐equivalence and the centro‐affine type of curves are introduced. All possible centro‐affine types are founded. For every centro‐affine type all invariant parametrizations of a curve are described. The problem ofGL(n,R)‐equivalence of curves is reduced to that of paths. © 2004 American Institute of Physics