We report a sensitive search for the rotational transitions of the carbon-chain alcohol HC 4 OH in the frequency range 21.2-46.7 GHz in the star-forming region L1527 and the dark cloud TMC-1. The motivation was laboratory detection of HC 4 OH by microwave spectroscopy. Despite achieving rms noise levels of several millikelvin in the antenna temperature using the 45 m telescope at Nobeyama Radio Observatory, the detection was not successful, leading to 3σ upper limits corresponding to the column densities of 2.0 × 10 12 and 5.6 × 10 12 cm −2 in L1527 and TMC-1, respectively. These upper limits indicate that [HC 4 OH]/[HC 5 N] ratios are less than 0.3 and 0.1 in L1527 and TMC-1, respectively, where HC 5 N is an HC 4 -chain cyanide and HC 4 OH is a hydroxide. These ratios suggest that the cyano carbon-chain molecule dominates the hydroxyl carbon-chain molecule in L1527 and TMC-1. This is contrary to the case of saturated compounds in hot cores, e.g., CH 3 OH and CH 3 CN, and can be a chemical feature of carbon-chain molecules in L1527 and TMC-1. In addition, the column densities of the "unsubstituted" carbon-chain molecule C 4 H and the sulfur-bearing molecules SO and HCS + were determined from detected lines in L1527.