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Revealing the large-scale structure from the 21cm intensity mapping surveysis only possible after the foreground cleaning. However, most current cleaningtechniques relying on the smoothness of the foreground spectrum lead to asevere side effect of removing the large-scale structure signal along the lineof sight. On the other hand, the clustering fossil, a coherent variation of thesmall-scale clustering over large scales, allows us to recover thelong-wavelength density modes from the off-diagonal correlation betweenshort-wavelength modes. In this paper, we study the requirements for anunbiased and optimal clustering-fossil estimator and show that (A) theestimator is unbiased only when using an accurate bispectrum model for thelong-short-short mode coupling and (B) including the connected four-pointcorrelation functions is essential for characterizing the noise power spectrumof the estimated long mode. The clustering fossil estimator based upon theleading-order bispectrum yields an unbiased estimation of the long-wavelength($k\lesssim 0.01~[h/{\rm Mpc}]$) modes with the cross-correlation coefficientof $0.7$ at redshifts $z=0$ to $3$.

Recovering the Missing Large-Scale Density Modes in 21cm Intensity Map from the Scalar-Type Clustering Fossils