diff --git a/thewalrus/decompositions.py b/thewalrus/decompositions.py
index 43967077..ad0e767b 100644
--- a/thewalrus/decompositions.py
+++ b/thewalrus/decompositions.py
@@ -210,6 +210,7 @@ def takagi(A, svd_order=True):
         list_vals.sort(reverse=svd_order)
         sorted_ls, permutation = zip(*list_vals)
         return np.array(sorted_ls), Uc[:, np.array(permutation)]
+
     # Find the element with the largest absolute value
     pos = np.unravel_index(np.argmax(np.abs(A)), (n, n))
     # Use it to find whether the input is a global phase times a real matrix
@@ -223,7 +224,7 @@ def takagi(A, svd_order=True):
     U = u @ sqrtm((v @ np.conjugate(u)).T)
     # The line above could be simplifed to the line below if the product v @ np.conjugate(u) is diagonal
     # Which it should be according to Caves http://info.phys.unm.edu/~caves/courses/qinfo-s17/lectures/polarsingularAutonne.pdf
-    # U = u * np.sqrt(0j + np.diag(np.conjugate(u) @ v))
+    # U = u * np.sqrt(0j + np.diag(v @ np.conjugate(u)))
     # This however breaks test_degenerate
     if svd_order is False:
         return d[::-1], U[:, ::-1]
diff --git a/thewalrus/symplectic.py b/thewalrus/symplectic.py
index 2583103c..0321e518 100644
--- a/thewalrus/symplectic.py
+++ b/thewalrus/symplectic.py
@@ -438,39 +438,6 @@ def is_symplectic(S, rtol=1e-05, atol=1e-08):
     return np.allclose(S.T @ Omega @ S, Omega, rtol=rtol, atol=atol)
 
 
-def autonne(A, rtol=1e-05, atol=1e-08, svd_order=True):
-    r"""Autonne-Takagi decomposition of a complex symmetric (not Hermitian!) matrix.
-
-    Args:
-        A (array): square, symmetric matrix
-        rtol (float): the relative tolerance parameter between ``A`` and ``A.T``
-        atol (float): the absolute tolerance parameter between ``A`` and ``A.T``
-        svd_order (boolean): whether to return result by ordering the singular values of ``A`` in descending (``True``) or asceding (``False``) order.
-
-    Returns:
-        tuple[array, array]: (r, U), where r are the singular values,
-        and U is the Autonne-Takagi unitary, such that :math:`A = U \diag(r) U^T`.
-    """
-    n, m = A.shape
-    if n != m:
-        raise ValueError("The input matrix is not square")
-    if not np.allclose(A, A.T, rtol=rtol, atol=atol):
-        raise ValueError("The input matrix is not symmetric")
-    Areal = A.real
-    Aimag = A.imag
-
-    B = np.empty((2 * n, 2 * n))
-    B[:n, :n] = Areal
-    B[n : 2 * n, :n] = Aimag
-    B[:n, n : 2 * n] = Aimag
-    B[n : 2 * n, n : 2 * n] = -Areal
-    vals, vects = np.linalg.eigh(B)
-    U = vects[:n, n : 2 * n] + 1j * vects[n : 2 * n, n : 2 * n]
-    if svd_order:
-        return (vals[n : 2 * n])[::-1], U[:, ::-1]
-    return vals[n : 2 * n], U
-
-
 def xxpp_to_xpxp(S):
     """Permutes the entries of the input from xxpp ordering to xpxp ordering.
 
diff --git a/thewalrus/tests/test_decompositions.py b/thewalrus/tests/test_decompositions.py
index 53975dd2..ab7deeff 100644
--- a/thewalrus/tests/test_decompositions.py
+++ b/thewalrus/tests/test_decompositions.py
@@ -396,6 +396,25 @@ def test_real_degenerate():
     assert np.allclose(U @ np.diag(rl) @ U.T, mat)
 
 
+@pytest.mark.parametrize("n", [5, 10, 50])
+@pytest.mark.parametrize("datatype", [np.complex128, np.float64])
+@pytest.mark.parametrize("svd_order", [True, False])
+def test_autonne_takagi(n, datatype, svd_order):
+    """Checks the correctness of the Autonne decomposition function"""
+    if datatype is np.complex128:
+        A = np.random.rand(n, n) + 1j * np.random.rand(n, n)
+    if datatype is np.float64:
+        A = np.random.rand(n, n)
+    A += A.T
+    r, U = takagi(A, svd_order=svd_order)
+    assert np.allclose(A, U @ np.diag(r) @ U.T)
+    assert np.all(r >= 0)
+    if svd_order is True:
+        assert np.all(np.diff(r) <= 0)
+    else:
+        assert np.all(np.diff(r) >= 0)
+
+
 @pytest.mark.parametrize("size", [10, 20, 100])
 def test_flat_phase(size):
     """Test that the correct decomposition is obtained even if the first entry is 0"""
diff --git a/thewalrus/tests/test_symplectic.py b/thewalrus/tests/test_symplectic.py
index 6afb0edd..40ff800b 100644
--- a/thewalrus/tests/test_symplectic.py
+++ b/thewalrus/tests/test_symplectic.py
@@ -12,7 +12,7 @@
 # See the License for the specific language governing permissions and
 # limitations under the License.
 """Symplectic tests"""
-# pylint: disable=no-self-use, assignment-from-no-return
+# pylint: disable=assignment-from-no-return
 import pytest
 
 import numpy as np
@@ -850,39 +850,6 @@ def test_sympmat(n):
     assert np.all(X == res)
 
 
-@pytest.mark.parametrize("n", [5, 10, 50])
-@pytest.mark.parametrize("datatype", [np.complex128, np.float64])
-@pytest.mark.parametrize("svd_order", [True, False])
-def test_autonne(n, datatype, svd_order):
-    """Checks the correctness of the Autonne decomposition function"""
-    if datatype is np.complex128:
-        A = np.random.rand(n, n) + 1j * np.random.rand(n, n)
-    if datatype is np.float64:
-        A = np.random.rand(n, n)
-    A += A.T
-    r, U = symplectic.autonne(A, svd_order=svd_order)
-    assert np.allclose(A, U @ np.diag(r) @ U.T)
-    assert np.all(r >= 0)
-    if svd_order is True:
-        assert np.all(np.diff(r) <= 0)
-    else:
-        assert np.all(np.diff(r) >= 0)
-
-
-def test_autonne_error():
-    """Tests the value errors of autonne"""
-    n = 10
-    m = 20
-    A = np.random.rand(n, m)
-    with pytest.raises(ValueError, match="The input matrix is not square"):
-        symplectic.autonne(A)
-    n = 10
-    m = 10
-    A = np.random.rand(n, m)
-    with pytest.raises(ValueError, match="The input matrix is not symmetric"):
-        symplectic.autonne(A)
-
-
 class TestPhaseSpaceFunctions:
     """Tests for the shared phase space operations"""