We report a novel crossover behavior in the long-range-ordered phase of a prototypical spin-1/2 Heisenberg antiferromagnetic ladder compound (C7H10N)(2)CuBr4. The staggered order was previously evidenced from a continuous and symmetric splitting of (NNMR)-N-14 spectral lines on lowering the temperature below Tc similar or equal to 330 mK, with a saturation towards. 150 mK. Unexpectedly, the split lines begin to further separate away below T* similar to 100mK, while the linewidth and the line shape remain completely invariable. This crossover behavior is further corroborated by the NMR relaxation rate T-1(-1) measurements. A very strong suppression reflecting the ordering, T-1(-1)similar to T-5.5, observed above T*, is replaced by T-1(-1) similar to T below T*. These original NMR features are indicative of the unconventional nature of the crossover, which may arise from a unique arrangement of the ladders into a spatially anisotropic and frustrated coupling network.