An experimental investigation of the odd-odd 162 Lu nucleus, following the 148 Sm( 19 F,5n) reaction at beam energy E lab ϭ112 MeV, has been performed through in-beam gamma-ray spectroscopy. It revealed three signature-split bands. The yrast band based on h 11/2 i 13/2 configuration exhibits anomalous signature splitting ͑the unfavored signature Routhian lying lower than the favored one͒ whose magnitude ⌬eЈϷ25 keV, is considerably reduced in contrast to sizable normal signature splitting ⌬eЈϷ125 and 60 keV observed in the yrast h 11/2 bands of the neighboring odd-A 161,163 Lu nuclei, respectively. The signature inversion in this band occurs at spin ϳ20ប (frequencyϭ0.37 MeV). The second signature-split band, observed above the band crossing associated with the alignment of a pair of i 13/2 quasineutrons, is a band based on the four-quasiparticle ͓h 11/2 ͓523͔7/2 Ϫ h 9/2 ͓521͔3/2 Ϫ (i 13/2 ) 2 ͔, i.e., EABA p (B p ), configuration. The third signature-split band is also likely to be a four-quasiparticle band with configuration similar to the second band but involving F quasineutron, i.e., FABA p (B p ). The experimental results are discussed in comparison with the existing data in the neighboring nuclei and in the framework of the cranking shell model. ͓S0556-2813͑97͒01809-8͔