Bernstein polynomials and Bezier curves play an important role in Computer Aided Geometric Design. Sev- eral generalizations of B ́ezier curves have been introduced in recent years. Aside from the natural generalizations represented by rational B ́ezier and B-spline curves, further generalizations have been investigated: among these, Polya polynomials [1, 2], q-B ́ezier curves [4], B ́ezier curves based on umbral calculus [5].

In this work we propose further results about generalized Bernstein operator which guarantees the second- order approximation property [3]. Specifically, a wider class of second-order operators is introduced, depending on a real parameter h.

Moreover we define and study a novel generalization of B ́ezier curves, based on such a new approach, showing numerical and graphical results.