A large number of color filter arrays (CFAs), periodic or aperiodic, have been proposed. To reconstruct images from all different CFAs and compare their imaging quality, a universal demosaicking method is needed. This paper proposes a new universal demosaicking method based on inter-pixel chrominance capture and optimal demosaicking transformation. It skips the commonly used step to estimate the luminance component at each pixel, and thus, avoids the associated estimation error. Instead, we directly use the acquired CFA color intensity at each pixel as an input component. Two independent chrominance components are estimated at each pixel based on the inter-pixel chrominance in the window, which is captured with the difference of CFA color values between the pixel of interest and its neighbors. Two mechanisms are employed for the accurate estimation: distance-related and edge-sensing weighting to reflect the confidence levels of the inter-pixel chrominance components, and pseudoinverse-based estimation from the components in a window. Then from the acquired CFA color component and two estimated chrominance components, the three primary colors are reconstructed by a linear color transform, which is optimized for the least transform error. Our experiments show that the proposed method is much better than other published universal demosaicking methods.