diff --git a/geomstats/geometry/special_euclidean.py b/geomstats/geometry/special_euclidean.py
index 2090419f1..32a15efca 100644
--- a/geomstats/geometry/special_euclidean.py
+++ b/geomstats/geometry/special_euclidean.py
@@ -1307,9 +1307,10 @@ class SpecialEuclideanMatrixLieAlgebra(MatrixLieAlgebra):
 
     def __init__(self, n):
         dim = int(n * (n + 1) / 2)
-        super(SpecialEuclideanMatrixLieAlgebra, self).__init__(dim, n)
+        super(SpecialEuclideanMatrixLieAlgebra, self).__init__(dim, n + 1)
 
         self.skew = SkewSymmetricMatrices(n)
+        self.n = n
 
     def _create_basis(self):
         """Create the canonical basis."""
@@ -1356,6 +1357,28 @@ class SpecialEuclideanMatrixLieAlgebra(MatrixLieAlgebra):
         belongs = gs.logical_and(belongs, all_zeros)
         return belongs
 
+    def random_point(self, n_samples=1, bound=1.0):
+        """Sample in the lie algebra with a uniform distribution in a box.
+
+        Parameters
+        ----------
+        n_samples : int
+            Number of samples.
+            Optional, default: 1.
+        bound : float
+            Side of hypercube support of the uniform distribution.
+            Optional, default: 1.0
+
+        Returns
+        -------
+        point : array-like, shape=[..., n + 1, n + 1]
+           Sample.
+        """
+        point = super(SpecialEuclideanMatrixLieAlgebra, self).random_point(
+            n_samples, bound
+        )
+        return self.projection(point)
+
     def projection(self, mat):
         """Project a matrix to the Lie Algebra.
 

diff --git a/tests/tests_geomstats/test_special_euclidean.py b/tests/tests_geomstats/test_special_euclidean.py
index 6c56a44b7..7361f960b 100644
--- a/tests/tests_geomstats/test_special_euclidean.py
+++ b/tests/tests_geomstats/test_special_euclidean.py
@@ -205,6 +205,12 @@ class TestSpecialEuclidean(geomstats.tests.TestCase):
             algebra = SpecialEuclideanMatrixLieAlgebra(n)
             self.assertEqual(int(n * (n + 1) / 2), algebra.dim)
 
+    def test_random_and_belongs_lie_algerba(self):
+        algebra = self.group.lie_algebra
+        point = algebra.random_point(2)
+        results = algebra.belongs(point)
+        self.assertTrue(gs.all(results))
+
     def test_belongs_lie_algebra(self):
         theta = gs.pi / 3
         vec_1 = gs.array([[0.0, -theta, 2.0], [theta, 0.0, 3.0], [0.0, 0.0, 0.0]])

SpecialEuclieanMatrixLieAlgebra randompoint has doesn't generate valid point
```
from geomstats.geometry.special_euclidean import SpecialEuclideanMatrixLieAlgebra 
algebra  = SpecialEuclideanMatrixLieAlgebra(2)
point = algebra.random_point(2) 
algebra.belongs(point)
```
tests/tests_geomstats/test_special_euclidean.py::TestSpecialEuclidean::test_random_and_belongs_lie_algerba
tests/tests_geomstats/test_special_euclidean.py::TestSpecialEuclidean::test_belongs tests/tests_geomstats/test_special_euclidean.py::TestSpecialEuclidean::test_random_point_and_belongs tests/tests_geomstats/test_special_euclidean.py::TestSpecialEuclidean::test_identity tests/tests_geomstats/test_special_euclidean.py::TestSpecialEuclidean::test_is_tangent tests/tests_geomstats/test_special_euclidean.py::TestSpecialEuclidean::test_to_tangent_vec_vectorization tests/tests_geomstats/test_special_euclidean.py::TestSpecialEuclidean::test_compose_and_inverse_matrix_form tests/tests_geomstats/test_special_euclidean.py::TestSpecialEuclidean::test_compose_vectorization tests/tests_geomstats/test_special_euclidean.py::TestSpecialEuclidean::test_inverse_vectorization tests/tests_geomstats/test_special_euclidean.py::TestSpecialEuclidean::test_compose_matrix_form tests/tests_geomstats/test_special_euclidean.py::TestSpecialEuclidean::test_left_exp_coincides tests/tests_geomstats/test_special_euclidean.py::TestSpecialEuclidean::test_right_exp_coincides tests/tests_geomstats/test_special_euclidean.py::TestSpecialEuclidean::test_basis_belongs tests/tests_geomstats/test_special_euclidean.py::TestSpecialEuclidean::test_basis_has_the_right_dimension tests/tests_geomstats/test_special_euclidean.py::TestSpecialEuclidean::test_belongs_lie_algebra tests/tests_geomstats/test_special_euclidean.py::TestSpecialEuclidean::test_basis_representation_is_correctly_vectorized tests/tests_geomstats/test_special_euclidean.py::TestSpecialEuclidean::test_left_metric_wrong_group tests/tests_geomstats/test_special_euclidean.py::TestSpecialEuclidean::test_exp_and_belongs tests/tests_geomstats/test_special_euclidean.py::TestSpecialEuclidean::test_log_and_is_tan tests/tests_geomstats/test_special_euclidean.py::TestSpecialEuclidean::test_exp_log tests/tests_geomstats/test_special_euclidean.py::TestSpecialEuclidean::test_parallel_transport tests/tests_geomstats/test_special_euclidean.py::TestSpecialEuclidean::test_lie_algebra_basis_belongs tests/tests_geomstats/test_special_euclidean.py::TestSpecialEuclidean::test_lie_algebra_projection_and_belongs tests/tests_geomstats/test_special_euclidean.py::TestSpecialEuclidean::test_basis_representation tests/tests_geomstats/test_special_euclidean.py::TestSpecialEuclidean::test_metrics_expected_point_type tests/tests_geomstats/test_special_euclidean.py::TestSpecialEuclidean::test_metric_left_invariant tests/tests_geomstats/test_special_euclidean.py::TestSpecialEuclidean::test_projection_and_belongs