The Debye relaxation is the main signal in the dielectric measurements of monoalcohols arising from the hydrogen-bonded superstructures, but its physics remains to be cleared. In this work, a monoalcohol of 4-methyl-2-pentanol is studied using dielectric spectroscopies recorded at high pressures. The dynamic parameters of the Debye and structural relaxations are extracted. The calculation of the Kirkwood factor of the Debye relaxation indicates chain-like H-bond molecular configurations. Remarkably, we found that both ratios of the relaxation strength and relaxation time between the Debye and structural dynamics, Δε
D/Δε
α
and τ
D/τ
α
, decreases upon compression, indicating a positive correlation. This is different from the results reported in primary 2-ethyl-1-hexanol and secondary 4-methyl-3-heptanol, where the two ratios are inversely correlated. The discussion and interpretation of these different results are provided.