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With large random catalog sizes (random-to-data objects\u2019 ratio <jats:italic>M<\/jats:italic>\u2004\u226b\u20041) the computational cost of the standard method is dominated by that of counting the data-random and random-random pairs, while the uncertainty of the estimate is dominated by that of data-data pairs. We present a method called Linear Construction (LC), where the covariance is estimated for small random catalogs with a size of <jats:italic>M<\/jats:italic>\u2004=\u20041 and <jats:italic>M<\/jats:italic>\u2004=\u20042, and the covariance for arbitrary <jats:italic>M<\/jats:italic> is constructed as a linear combination of the two. We show that the LC covariance estimate is unbiased. We validated the method with PINOCCHIO simulations in the range <jats:italic>r<\/jats:italic>\u2004=\u200420\u2005\u2212\u2005200 <jats:italic>h<\/jats:italic><jats:sup>\u22121<\/jats:sup> Mpc. With <jats:italic>M<\/jats:italic>\u2004=\u200450 and with 2 <jats:italic>h<\/jats:italic><jats:sup>\u22121<\/jats:sup> Mpc bins, the theoretical speedup of the method is a factor of 14. 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