The best linear unbiased prediction (BLUP), derived from the linear mixed model (LMM), has been popularly used to estimate animal and plant breeding values (BVs) for a few decades. Conventional BLUP has a constraint that BVs are estimated from the assumed covariance among unknown BVs, namely conventional BLUP assumes that its covariance matrix is a $\lambda$K, in which $\lambda$ is a coefficient that leads to the minimum mean square error of the LMM, and K is a genetic relationship matrix. The uncertainty regarding the use of $\lambda$K inconventional BLUP was recognized by past studies, but it has not been sufficiently investigated. This study was motivated to answer the following question: is it indeed reasonable to use a $\lambda$K in conventional BLUP? The mathematical investigation concluded: (i) the use of a $\lambda$K in conventional BLUP biases the estimated BVs, and (ii) the objective BLUP, mathematically derived from the LMM, has the same representation as the least squares.