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We conducted a high-sensitivity radio detection survey for 40 narrow-line Seyfert 1 (NLS1) galaxies using a very long baseline interferometry (VLBI) technique at 22GHz through phase-referencing long-time integration and using a newly developing recorder with a data rate of 8Gbps, which is a candidate of the next generation VLBI data recording systems of the Japanese VLBI Network. The baseline sensitivity was typically a few mJy. The observations resulted in a detection rate of 12/40 for our radio-selected NLS1 sample: 11 out of the 12 detected NLS1s showed inverted radio spectra between 1.4 and 22GHz on the basis of the Very Large Array flux densities and the VLBI detections. These high fractions suggest that a compact radio core with a high brightness temperature is frequently associated with NLS1 nuclei. On the other hand, at least half of the sample indicated apparently steep spectra even with the limited VLBI sensitivity. Both the inverted and the steep spectrum radio sources are included in the NLS1 population. [ABSTRACT FROM AUTHOR]