In some OFDR implementations it is advantageous to use sinusoidal frequency tuning and to work in the linear range of the sinusoid. For a given scan frequency this limits the maximum length of the interrogated fiber. We propose a new method which allows exceedingly large delays while maintaining high scan rates. It is based on the observation that delay of half the scan period yields linearly frequency modulated (LFM) signals at the OFDR receiver. Using Fractional Fourier Transform (FrFT) for processing the raw data enables measurement of the z-dependent reflection at long ranges with high resolution and high scan rates.