A self-synchronizing scrambler for high bit rates has a number of scrambler stages supplied in parallel with bits of a signal to be scrambled, each scrambler stage having a series-connected pair of modulo-2 adders, and at least one shift register. A selected number of scrambler stages in the scrambler may include an additional shift register depending upon the number p of parallel bits in the signal to be scrambled, and the total number n of shift registers in the scrambler. The number of scrambler stages having two shift registers is n-p and the number of following scrambler stages having one shift register is 2 p-n. For suppressing short periods, a further modulo-2 adder can be connected between the original two modulo-2 adders, the additional modulo-2 adder inverting at least one bit of the signal for the short periods.