diff --git a/CHANGELOG.md b/CHANGELOG.md
index b4c8d3f..fc6bcbe 100644
--- a/CHANGELOG.md
+++ b/CHANGELOG.md
@@ -8,6 +8,8 @@ The format is based on [Keep a Changelog](https://keepachangelog.com/en/1.0.0/).
 ### Added
 
 - Python3 shebang line to script in tools ([408](https://github.com/pdfminer/pdfminer.six/pull/408)
+### Fixed
+- Fix ordering of textlines within a textbox when `boxes_flow=None` ([#411](https://github.com/pdfminer/pdfminer.six/issues/411))
 
 ## [20200402]
 
diff --git a/pdfminer/layout.py b/pdfminer/layout.py
index cc0c88d..8bce26b 100644
--- a/pdfminer/layout.py
+++ b/pdfminer/layout.py
@@ -798,6 +798,9 @@ class LTLayoutContainer(LTContainer):
             obj.analyze(laparams)
         textboxes = list(self.group_textlines(laparams, textlines))
         if laparams.boxes_flow is None:
+            for textbox in textboxes:
+                textbox.analyze(laparams)
+
             def getkey(box):
                 if isinstance(box, LTTextBoxVertical):
                     return (0, -box.x1, -box.y0)
diff --git a/samples/simple4.pdf b/samples/simple4.pdf
new file mode 100644
index 0000000..14b6fc5
Binary files /dev/null and b/samples/simple4.pdf differ
diff --git a/tests/test_highlevel_extracttext.py b/tests/test_highlevel_extracttext.py
index 9ed7224..86788a0 100644
--- a/tests/test_highlevel_extracttext.py
+++ b/tests/test_highlevel_extracttext.py
@@ -1,8 +1,8 @@
 import unittest
 
 from helpers import absolute_sample_path
-from pdfminer.high_level import extract_text
-from pdfminer.layout import LAParams
+from pdfminer.high_level import extract_text, extract_pages
+from pdfminer.layout import LAParams, LTTextContainer
 
 
 def run_with_string(sample_path, laparams=None):
@@ -24,11 +24,12 @@ test_strings = {
     "simple1.pdf": "Hello \n\nWorld\n\nHello \n\nWorld\n\n"
                    "H e l l o  \n\nW o r l d\n\n"
                    "H e l l o  \n\nW o r l d\n\n\f",
-    "simple1.pdf_no_boxes_flow": "Hello \nWorld\nHello \nWorld\n"
-                                 "H e l l o  \nW o r l d\n"
-                                 "H e l l o  \nW o r l d\n\f",
+    "simple1.pdf_no_boxes_flow": "Hello \n\nWorld\n\nHello \n\nWorld\n\n"
+                                 "H e l l o  \n\nW o r l d\n\n"
+                                 "H e l l o  \n\nW o r l d\n\n\f",
     "simple2.pdf": "\f",
     "simple3.pdf": "Hello\n\nHello\n\nWorld\n\nWorld\n\n\f",
+    "simple4.pdf": "Text1\nText2\nText3\n\n\f"
 }
 
 
@@ -53,6 +54,11 @@ class TestExtractText(unittest.TestCase):
         s = run_with_string(test_file)
         self.assertEqual(s, test_strings[test_file])
 
+    def test_simple4_with_string(self):
+        test_file = "simple4.pdf"
+        s = run_with_string(test_file)
+        self.assertEqual(s, test_strings[test_file])
+
     def test_simple1_with_file(self):
         test_file = "simple1.pdf"
         s = run_with_file(test_file)
@@ -68,6 +74,54 @@ class TestExtractText(unittest.TestCase):
         s = run_with_file(test_file)
         self.assertEqual(s, test_strings[test_file])
 
+    def test_simple4_with_file(self):
+        test_file = "simple4.pdf"
+        s = run_with_file(test_file)
+        self.assertEqual(s, test_strings[test_file])
+
+
+class TestExtractPages(unittest.TestCase):
+    def _get_test_file_path(self):
+        test_file = "simple4.pdf"
+        return absolute_sample_path(test_file)
+
+    def test_line_margin(self):
+        # The lines have margin 0.2 relative to the height.
+        # Extract with line_margin 0.19 should break into 3 separate textboxes.
+        pages = list(extract_pages(
+            self._get_test_file_path(), laparams=LAParams(line_margin=0.19)))
+        self.assertEqual(len(pages), 1)
+        page = pages[0]
+
+        elements = [element for element in page
+                    if isinstance(element, LTTextContainer)]
+        self.assertEqual(len(elements), 3)
+        self.assertEqual(elements[0].get_text(), "Text1\n")
+        self.assertEqual(elements[1].get_text(), "Text2\n")
+        self.assertEqual(elements[2].get_text(), "Text3\n")
+
+        # Extract with line_margin 0.21 should merge into one textbox.
+        pages = list(extract_pages(
+            self._get_test_file_path(), laparams=LAParams(line_margin=0.21)))
+        self.assertEqual(len(pages), 1)
+        page = pages[0]
+
+        elements = [element for element in page
+                    if isinstance(element, LTTextContainer)]
+        self.assertEqual(len(elements), 1)
+        self.assertEqual(elements[0].get_text(), "Text1\nText2\nText3\n")
+
+    def test_no_boxes_flow(self):
+        pages = list(extract_pages(
+            self._get_test_file_path(), laparams=LAParams(boxes_flow=None)))
+        self.assertEqual(len(pages), 1)
+        page = pages[0]
+
+        elements = [element for element in page
+                    if isinstance(element, LTTextContainer)]
+        self.assertEqual(len(elements), 1)
+        self.assertEqual(elements[0].get_text(), "Text1\nText2\nText3\n")
+
 
 if __name__ == "__main__":
     unittest.main()