diff --git a/doc/whats-new.rst b/doc/whats-new.rst
index 1d00cb369d1..9ee350e084d 100644
--- a/doc/whats-new.rst
+++ b/doc/whats-new.rst
@@ -76,6 +76,10 @@ Bug fixes
 
 Documentation
 ~~~~~~~~~~~~~
+- update the docstring of :py:meth:`DataArray.assign_coords` : clarify how to
+  add a new coordinate to an existing dimension and illustrative example
+  (:issue:`3952`, :pull:`3958`) By
+  `Etienne Combrisson <https://github.com/EtienneCmb>`_.
 - update the docstring of :py:meth:`Dataset.diff` and
   :py:meth:`DataArray.diff` so it does document the ``dim``
   parameter as required. (:issue:`1040`, :pull:`3909`)
diff --git a/xarray/core/common.py b/xarray/core/common.py
index a003642076f..e8c43e964aa 100644
--- a/xarray/core/common.py
+++ b/xarray/core/common.py
@@ -399,10 +399,14 @@ def assign_coords(self, coords=None, **coords_kwargs):
         Parameters
         ----------
         coords : dict, optional
-            A dict with keys which are variables names. If the values are
-            callable, they are computed on this object and assigned to new
-            coordinate variables. If the values are not callable,
-            (e.g. a ``DataArray``, scalar, or array), they are simply assigned.
+            A dict where the keys are the names of the coordinates
+            with the new values to assign. If the values are callable, they are
+            computed on this object and assigned to new coordinate variables.
+            If the values are not callable, (e.g. a ``DataArray``, scalar, or
+            array), they are simply assigned. A new coordinate can also be
+            defined and attached to an existing dimension using a tuple with
+            the first element the dimension name and the second element the
+            values for this new coordinate.
 
         **coords_kwargs : keyword, value pairs, optional
             The keyword arguments form of ``coords``.
@@ -440,10 +444,23 @@ def assign_coords(self, coords=None, **coords_kwargs):
         Coordinates:
           * lon      (lon) int64 -2 -1 0 1
 
+        New coordinate can also be attached to an existing dimension:
+
+        >>> lon_2 = np.array([300, 289, 0, 1])
+        >>> da.assign_coords(lon_2=('lon', lon_2))
+        <xarray.DataArray (lon: 4)>
+        array([0.28298 , 0.667347, 0.657938, 0.177683])
+        Coordinates:
+          * lon      (lon) int64 358 359 0 1
+            lon_2    (lon) int64 300 289 0 1
+
+        Note that the same result can also be obtained with a dict e.g.
+        >>> _ = da.assign_coords({"lon_2": ('lon', lon_2)})
+
         Notes
         -----
-        Since ``coords_kwargs`` is a dictionary, the order of your arguments may
-        not be preserved, and so the order of the new variables is not well
+        Since ``coords_kwargs`` is a dictionary, the order of your arguments
+        may not be preserved, and so the order of the new variables is not well
         defined. Assigning multiple variables within the same ``assign_coords``
         is possible, but you cannot reference other variables created within
         the same ``assign_coords`` call.