diff --git a/src/linalg.jl b/src/linalg.jl
index f4feb7c2..0d1cfc66 100644
--- a/src/linalg.jl
+++ b/src/linalg.jl
@@ -1494,12 +1494,11 @@ factorize(A::AbstractSparseMatrixCSC) = _sparse_factorize(_factorize_choice, A)
 
 function factorize(A::RealHermSymComplexHerm{<:Union{Float32,Float64},<:AbstractSparseMatrixCSC})
     F = cholesky(A; check = false)
-    if LinearAlgebra.issuccess(F)
-        return F
-    else
-        ldlt!(F, A)
-        return F
-    end
+    LinearAlgebra.issuccess(F) && return F
+    ldlt!(F, A; check = false)
+    LinearAlgebra.issuccess(F) && return F
+    # an indefinite matrix may need pivoting, which only the LU does, as in `\`
+    return lu(A)
 end
 
 eigen(A::AbstractSparseMatrixCSC) =
diff --git a/test/solvers/issues.jl b/test/solvers/issues.jl
index 588c8acb..7154b74f 100644
--- a/test/solvers/issues.jl
+++ b/test/solvers/issues.jl
@@ -241,4 +241,9 @@ end
     @test ldiv!(lu(A), ComplexF32[1, 2]) ≈ ComplexF32.(Matrix(A) \ [1, 2])
 end
 
+@testset "factorize of an indefinite Hermitian matrix whose LDLt needs pivoting" begin
+    b = [1.0, 2.0]
+    @test factorize(sparse([0.0 1; 1 0])) \ b ≈ [0.0 1; 1 0] \ b
+end
+
 end # module