diff --git a/doc/source/whatsnew/v1.3.0.rst b/doc/source/whatsnew/v1.3.0.rst
index 74710ca48308c..6099ab4a9c365 100644
--- a/doc/source/whatsnew/v1.3.0.rst
+++ b/doc/source/whatsnew/v1.3.0.rst
@@ -796,7 +796,8 @@ I/O
 - Bug in :func:`read_sas` raising ``ValueError`` when ``datetimes`` were null (:issue:`39725`)
 - Bug in :func:`read_excel` dropping empty values from single-column spreadsheets (:issue:`39808`)
 - Bug in :func:`read_excel` raising ``AttributeError`` with ``MultiIndex`` header followed by two empty rows and no index, and bug affecting :func:`read_excel`, :func:`read_csv`, :func:`read_table`, :func:`read_fwf`, and :func:`read_clipboard` where one blank row after a ``MultiIndex`` header with no index would be dropped (:issue:`40442`)
-- Bug in :meth:`DataFrame.to_string` misplacing the truncation column when ``index=False`` (:issue:`40907`)
+- Bug in :meth:`DataFrame.to_string` misplacing the truncation column when ``index=False`` (:issue:`40904`)
+- Bug in :meth:`DataFrame.to_string` adding an extra dot and misaligning the truncation row when ``index=False`` (:issue:`40904`)
 - Bug in :func:`read_orc` always raising ``AttributeError`` (:issue:`40918`)
 - Bug in the conversion from pyarrow to pandas (e.g. for reading Parquet) with nullable dtypes and a pyarrow array whose data buffer size is not a multiple of dtype size (:issue:`40896`)
 
diff --git a/pandas/io/formats/string.py b/pandas/io/formats/string.py
index de53646b5f95f..20fc84a4df303 100644
--- a/pandas/io/formats/string.py
+++ b/pandas/io/formats/string.py
@@ -74,11 +74,14 @@ def _insert_dot_separators(self, strcols: List[List[str]]) -> List[List[str]]:
 
         return strcols
 
+    @property
+    def _adjusted_tr_col_num(self) -> int:
+        return self.fmt.tr_col_num + 1 if self.fmt.index else self.fmt.tr_col_num
+
     def _insert_dot_separator_horizontal(
         self, strcols: List[List[str]], index_length: int
     ) -> List[List[str]]:
-        tr_col_num = self.fmt.tr_col_num + 1 if self.fmt.index else self.fmt.tr_col_num
-        strcols.insert(tr_col_num, [" ..."] * index_length)
+        strcols.insert(self._adjusted_tr_col_num, [" ..."] * index_length)
         return strcols
 
     def _insert_dot_separator_vertical(
@@ -90,7 +93,7 @@ def _insert_dot_separator_vertical(
             cwidth = self.adj.len(col[row_num])
 
             if self.fmt.is_truncated_horizontally:
-                is_dot_col = ix == self.fmt.tr_col_num + 1
+                is_dot_col = ix == self._adjusted_tr_col_num
             else:
                 is_dot_col = False
 
@@ -99,7 +102,7 @@ def _insert_dot_separator_vertical(
             else:
                 dots = ".."
 
-            if ix == 0:
+            if ix == 0 and self.fmt.index:
                 dot_mode = "left"
             elif is_dot_col:
                 cwidth = 4
diff --git a/pandas/tests/io/formats/test_to_string.py b/pandas/tests/io/formats/test_to_string.py
index f9b3cac3527ef..65a438ad6108b 100644
--- a/pandas/tests/io/formats/test_to_string.py
+++ b/pandas/tests/io/formats/test_to_string.py
@@ -107,37 +107,51 @@ def test_format_remove_leading_space_dataframe(input_array, expected):
 
 
 @pytest.mark.parametrize(
-    "max_cols, expected",
+    "max_cols, max_rows, expected",
     [
         (
             10,
-            [
-                " 0   1   2   3   4   ...  6   7   8   9   10",
-                "  0   0   0   0   0  ...   0   0   0   0   0",
-                "  0   0   0   0   0  ...   0   0   0   0   0",
-            ],
+            None,
+            " 0   1   2   3   4   ...  6   7   8   9   10\n"
+            "  0   0   0   0   0  ...   0   0   0   0   0\n"
+            "  0   0   0   0   0  ...   0   0   0   0   0\n"
+            "  0   0   0   0   0  ...   0   0   0   0   0\n"
+            "  0   0   0   0   0  ...   0   0   0   0   0",
+        ),
+        (
+            None,
+            2,
+            " 0   1   2   3   4   5   6   7   8   9   10\n"
+            "  0   0   0   0   0   0   0   0   0   0   0\n"
+            " ..  ..  ..  ..  ..  ..  ..  ..  ..  ..  ..\n"
+            "  0   0   0   0   0   0   0   0   0   0   0",
+        ),
+        (
+            10,
+            2,
+            " 0   1   2   3   4   ...  6   7   8   9   10\n"
+            "  0   0   0   0   0  ...   0   0   0   0   0\n"
+            " ..  ..  ..  ..  ..  ...  ..  ..  ..  ..  ..\n"
+            "  0   0   0   0   0  ...   0   0   0   0   0",
         ),
         (
             9,
-            [
-                " 0   1   2   3   ...  7   8   9   10",
-                "  0   0   0   0  ...   0   0   0   0",
-                "  0   0   0   0  ...   0   0   0   0",
-            ],
+            2,
+            " 0   1   2   3   ...  7   8   9   10\n"
+            "  0   0   0   0  ...   0   0   0   0\n"
+            " ..  ..  ..  ..  ...  ..  ..  ..  ..\n"
+            "  0   0   0   0  ...   0   0   0   0",
         ),
         (
             1,
-            [
-                " 0  ...",
-                " 0  ...",
-                " 0  ...",
-            ],
+            1,
+            " 0  ...\n 0  ...\n..  ...",
         ),
     ],
 )
-def test_truncation_col_placement_no_index(max_cols, expected):
-    df = DataFrame([[0] * 11] * 2)
-    assert df.to_string(index=False, max_cols=max_cols).split("\n") == expected
+def test_truncation_no_index(max_cols, max_rows, expected):
+    df = DataFrame([[0] * 11] * 4)
+    assert df.to_string(index=False, max_cols=max_cols, max_rows=max_rows) == expected
 
 
 def test_to_string_unicode_columns(float_frame):