Context : For direct imaging of exoplanets , a stellar coronagraph helps to remove the image of an observed bright star by attenuating the diffraction effects caused by the telescope aperture of diameter D . The Dual Zone Phase Mask ( DZPM ) coronagraph constitutes a promising concept since it theoretically offers a small inner working angle ( IWA \sim \lambda _ { 0 } / D where \lambda _ { 0 } denotes the central wavelength of the spectral range \Delta \lambda ) , good achromaticity and high starlight rejection , typically reaching a 10 ^ { 6 } contrast at 5 \lambda _ { 0 } / D from the star over a spectral bandwidth \Delta \lambda / \lambda _ { 0 } of 25 % ( similar to H-band ) . This last value proves to be encouraging for broadband imaging of young and warm Jupiter-like planets . Aims : Contrast levels higher than 10 ^ { 6 } are however required for the observation of older and/or less massive companions over a finite spectral bandwidth . An achromatization improvement of the DZPM coronagraph is therefore mandatory to reach such performance . Methods : In its design , the DZPM coronagraph uses a grey ( or achromatic ) apodization . We propose to replace it by a colored apodization to increase the performance of this coronagraphic system over a large spectral range . This innovative concept , called Colored Apodizer Phase Mask ( CAPM ) coronagraph , is defined with some design parameters optimized to reach the best contrast in the exoplanet search area . Once this done , we study the performance of the CAPM coronagraph in the presence of different errors to evaluate the sensitivity of our concept . Results : A 2.5 \operatorname { mag } contrast gain is estimated from the performance provided by the CAPM coronagraph with respect to that of the DZPM coronagraph . A 2.2 \cdot 10 ^ { -8 } intensity level at 5 \lambda _ { 0 } / D separation is then theoretically achieved with the CAPM coronagraph in the presence of a clear circular aperture and a 25 % bandwidth . In addition , our studies show that our concept is less sensitive to low than high-order aberrations for a given value of rms wavefront errors . Conclusions :