  A new mechanism for relaxing the nuclear magnetic moments, in which a pair of
spin-polarized BCS quasiparticles is emitted or absorbed, and which dominates
at low temperature, is identified in type-II d-wave superconductors in an
external magnetic field above Hc1. The results of the theory are compared with
the NMR experiments on YBCO in high magnetic fields and found to agree without
invoking antiferromagnetic order in the vortex core.
