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We present the radio properties of 66 spectroscopically confirmed normal star-forming galaxies (SFGs) at 4.4 <z< 5.9 in the COSMOS field that were [Cii]-detected in the Atacama Large Millimeter/submillimeter Array Large Program to INvestigate [Cii] at Early times (ALPINE). We separate these galaxies (“Cii-detected-all”) into lower-redshift (“Cii-detected-lz”; 〈z〉 = 4.5) and higher-redshift (“Cii-detected-hz”; 〈z〉 = 5.6) subsamples, and stack multiwavelength imaging for each subsample from X-ray to radio bands. A radio signal is detected in the stacked 3 GHz images of the Cii-detected-all and lz samples at ≳3σ. We find that the infrared–radio correlation of our sample, quantified byq_TIR, is lower than the local relation for normal SFGs at a ∼3σsignificance level, and is instead broadly consistent with that of bright submillimeter galaxies at 2 <z< 5. Neither of these samples show evidence of dominant active galactic nucleus activity in their stacked spectral energy distributions (SEDs), UV spectra, or stacked X-ray images. Although we cannot rule out the possible effects of the assumed spectral index and applied infrared SED templates in causing these differences, at least partially, the lower obscured fraction of star formation than at lower redshift can alleviate the tension between our stackedq_TIRs and those of local normal SFGs. It is possible that the dust buildup, which primarily governs the infrared emission, in addition to older stellar populations, has not had enough time to occur fully in these galaxies, whereas the radio emission can respond on a more rapid timescale. Therefore, we might expect a lowerq_TIRto be a general property of high-redshift SFGs.