We report the discovery of a new group of double-periodic stars in the OGLE Galactic bulge photometry .
In 38 stars identified as fundamental mode RR Lyrae and 4 classified as the first-overtone RR Lyrae , we detected additional shorter periodicity .
Periods of the dominant variability in the newly discovered group are 0.28 < P _ { D } < 0.41 days .
Period ratios ( 0.68 - 0.72 ) are smaller than the period ratios of the Galactic bulge RRd stars .
The typical amplitude ratio ( of the additional to the dominant periodicity ) is 20 % for the stars identified as fundamental mode RR Lyrae and 50 % for stars classified as the first-overtone RR Lyrae .
Ten stars from our sample exhibit equidistant peaks in the frequency spectrum , that suggest the Blazhko-type modulation of the main pulsation frequency and/or the additional periodicity .
The Fourier coefficients R _ { \mathrm { 21 } } and R _ { \mathrm { 31 } } are one of the lowest among fundamental mode RR Lyrae stars , but among the highest for the first-overtone pulsators .
For the phase Fourier coefficients \varphi _ { \mathrm { 21 } } and \varphi _ { \mathrm { 31 } } , our stars lie in between RRab and RRc stars .
Discussed stars were compared with the radial , linear pulsation models .
Their position in the Petersen diagram can not be reproduced assuming that two radial modes are excited and their physical parameters are similar to that characteristic for RR Lyrae stars .
The non-radial mode scenario also faces difficulties .
We conclude that the dominant variability is most likely due to pulsation in the radial fundamental mode including stars classified as the first overtone mode pulsators .
At this point , we can not explain the nature of the additional periodicity .
Even more , classification of the stars as RR Lyrae should be treated as tentative .