A new frequency-modulated continuous wave modulation scheme, which gives correct results even when the Doppler shift is larger than the frequency difference associated with the range, is presented and tested with a tunable laser diode and fiber-based system. By inserting a constant frequency region in the modulation scheme, both the magnitude and the sign of all beat frequencies can be determined. When they are known, the correct frequency difference as a result of the range can be calculated. This new scheme gives more freedom when choosing the modulation parameters of the laser, because increasing the modulation frequency, and/or the frequency sweep, to avoid ambiguities resulting from a large Doppler shift no longer becomes necessary. This is especially useful when using a somewhat cheaper laser diode source, since the maximum obtainable modulation frequency and frequency sweep can be somewhat limited. The suggested modulation scheme makes it possible to use some laser diodes in an application they otherwise would not be suited for.