  We investigate the local descents for special orthogonal groups over p-adic
local fields of characteristic zero, and obtain an explicit spectral
decomposition of the local descents at the first occurrence index in terms of
the local Langlands data via the explicit local Langlands correspondence and
explicit calculations of relevant local root numbers. The main result can be
regarded as a refinement of the local Gan-Gross-Prasad conjecture.
