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In this paper we derive the matrix of transformation of the Jacobi polynomial basis form into the Bernstein polynomial basis of the same degree n and vice versa. This enables us to combine the superior least-squares performance of the Jacobi polynomials with the geometrical insight of the Bernstein form. Application to the inversion of the Bézier curves is given. 2000 Mathematics Subject Classification: 41A10; 33C45; 65D17.doi:10.2478/cmam-2004-0012 fatcat:clukeljx5jdffox5wfgrkqbepu