diff --git a/stdlib/LinearAlgebra/src/bunchkaufman.jl b/stdlib/LinearAlgebra/src/bunchkaufman.jl
index a238c43965dae..65e4c8d2e8463 100644
--- a/stdlib/LinearAlgebra/src/bunchkaufman.jl
+++ b/stdlib/LinearAlgebra/src/bunchkaufman.jl
@@ -125,7 +125,7 @@ size(B::BunchKaufman, d::Integer) = size(getfield(B, :LD), d)
 issymmetric(B::BunchKaufman) = B.symmetric
 ishermitian(B::BunchKaufman) = !B.symmetric
 
-function _ipiv2perm_bk(v::AbstractVector{T}, maxi::Integer, uplo::AbstractChar) where T
+function _ipiv2perm_bk(v::AbstractVector{T}, maxi::Integer, uplo::AbstractChar, rook::Bool) where T
     require_one_based_indexing(v)
     p = T[1:maxi;]
     uploL = uplo == 'L'
@@ -137,11 +137,16 @@ function _ipiv2perm_bk(v::AbstractVector{T}, maxi::Integer, uplo::AbstractChar)
             p[i], p[vi] = p[vi], p[i]
             i += uploL ? 1 : -1
         else # the 2x2 blocks
+            if rook
+                p[i], p[-vi] = p[-vi], p[i]
+            end
             if uploL
-                p[i + 1], p[-vi] = p[-vi], p[i + 1]
+                vp = rook ? -v[i+1] : -vi
+                p[i + 1], p[vp] = p[vp], p[i + 1]
                 i += 2
             else # 'U'
-                p[i - 1], p[-vi] = p[-vi], p[i - 1]
+                vp = rook ? -v[i-1] : -vi
+                p[i - 1], p[vp] = p[vp], p[i - 1]
                 i -= 2
             end
         end
@@ -208,7 +213,7 @@ julia> F.U*F.D*F.U' - F.P*A*F.P'
 function getproperty(B::BunchKaufman{T}, d::Symbol) where {T<:BlasFloat}
     n = size(B, 1)
     if d == :p
-        return _ipiv2perm_bk(getfield(B, :ipiv), n, getfield(B, :uplo))
+        return _ipiv2perm_bk(getfield(B, :ipiv), n, getfield(B, :uplo), B.rook)
     elseif d == :P
         return Matrix{T}(I, n, n)[:,invperm(B.p)]
     elseif d == :L || d == :U || d == :D
diff --git a/stdlib/LinearAlgebra/test/bunchkaufman.jl b/stdlib/LinearAlgebra/test/bunchkaufman.jl
index 40784d01bb0e2..7a55b0242e5b9 100644
--- a/stdlib/LinearAlgebra/test/bunchkaufman.jl
+++ b/stdlib/LinearAlgebra/test/bunchkaufman.jl
@@ -145,6 +145,12 @@ end
     @test F\v5 == F\v6[1:5]
 end
 
+@testset "issue #32080" begin
+    A = Symmetric([-5 -9 9; -9 4 1; 9 1 2])
+    B = bunchkaufman(A, true)
+    @test B.U * B.D * B.U' ≈ A[B.p, B.p]
+end
+
 @test_throws DomainError logdet(bunchkaufman([-1 -1; -1 1]))
 @test logabsdet(bunchkaufman([8 4; 4 2]; check = false))[1] == -Inf
 @test isa(bunchkaufman(Symmetric(ones(0,0))), BunchKaufman) # 0x0 matrix