In this work the formation of laser-induced periodic surface structures (LIPSS) on a titanium surface upon irradiation by linearly polarized femtosecond (fs) laser pulses with a repetition rate of 1 kHz in air environment was studied experimentally. In particular, the dependence of high-spatial-frequency-LIPSS (HSFL) characteristics on various laser parameters: fluence, pulse number, wavelength (800 nm and 400 nm), pulse duration (10 fs - 550 fs), and polarization was studied in detail. In comparison with low-spatial-frequency-LIPSS (LSFL), the HSFL emerge at a much lower fluence with orientation perpendicular to the ridges of the LSFL. It was observed that these two types of LIPSS demonstrate different fluence, shot number and wavelength dependencies, which suggest their origin is different. Therefore, the HSFL formation mechanism cannot be described by the widely accepted interference model developed for describing LSFL formation.