  We present a new construction of Radon curves which only uses convexity
methods. In other words, it does not rely on an auxiliary Euclidean background
metric (as in the classical works of J. Radon, W. Blaschke, G. Birkhoff, and M.
M. Day), and also it does not use typical methods from plane Minkowski Geometry
(as proposed by H. Martini and K. J. Swanepoel). We also discuss some
properties of normed planes whose unit circle is a Radon curve and give
characterizations of Radon curves only in terms of Convex Geometry.
