diff --git a/src/Spout/Reader/XLSX/RowIterator.php b/src/Spout/Reader/XLSX/RowIterator.php
index c7491ac..a7c70e6 100644
--- a/src/Spout/Reader/XLSX/RowIterator.php
+++ b/src/Spout/Reader/XLSX/RowIterator.php
@@ -55,6 +55,9 @@ class RowIterator implements IteratorInterface
     /** @var int The number of columns the sheet has (0 meaning undefined) */
     protected $numColumns = 0;
 
+    /** @var int Last column index processed (zero-based) */
+    protected $lastColumnIndexProcessed = -1;
+
     /**
      * @param string $filePath Path of the XLSX file being read
      * @param string $sheetDataXMLFilePath Path of the sheet data XML file as in [Content_Types].xml
@@ -144,6 +147,9 @@ class RowIterator implements IteratorInterface
                 } else if ($this->xmlReader->isPositionedOnStartingNode(self::XML_NODE_ROW)) {
                     // Start of the row description
 
+                    // Reset index of the last processed column
+                    $this->lastColumnIndexProcessed = -1;
+
                     // Read spans info if present
                     $numberOfColumnsForRow = $this->numColumns;
                     $spans = $this->xmlReader->getAttribute(self::XML_ATTRIBUTE_SPANS); // returns '1:5' for instance
@@ -155,12 +161,13 @@ class RowIterator implements IteratorInterface
 
                 } else if ($this->xmlReader->isPositionedOnStartingNode(self::XML_NODE_CELL)) {
                     // Start of a cell description
-                    $currentCellIndex = $this->xmlReader->getAttribute(self::XML_ATTRIBUTE_CELL_INDEX);
-                    $currentColumnIndex = CellHelper::getColumnIndexFromCellIndex($currentCellIndex);
+                    $currentColumnIndex = $this->getCellIndex($this->xmlReader);
 
                     $node = $this->xmlReader->expand();
                     $rowData[$currentColumnIndex] = $this->getCellValue($node);
 
+                    $this->lastColumnIndexProcessed = $currentColumnIndex;
+
                 } else if ($this->xmlReader->isPositionedOnEndingNode(self::XML_NODE_ROW)) {
                     // End of the row description
                     // If needed, we fill the empty cells
@@ -182,6 +189,21 @@ class RowIterator implements IteratorInterface
         $this->rowDataBuffer = $rowData;
     }
 
+    /**
+     * @param \Box\Spout\Reader\Wrapper\XMLReader $xmlReader XMLReader object, positioned on a "<c>" tag
+     * @return int
+     * @throws \Box\Spout\Common\Exception\InvalidArgumentException When the given cell index is invalid
+     */
+    protected function getCellIndex($xmlReader)
+    {
+        // Get "r" attribute if present (from something like <c r="A1"...>
+        $currentCellIndex = $xmlReader->getAttribute(self::XML_ATTRIBUTE_CELL_INDEX);
+
+        return ($currentCellIndex !== null) ?
+                CellHelper::getColumnIndexFromCellIndex($currentCellIndex) :
+                $this->lastColumnIndexProcessed + 1;
+    }
+
     /**
      * Returns the (unescaped) correctly marshalled, cell value associated to the given XML node.
      *
diff --git a/tests/Spout/Reader/XLSX/ReaderTest.php b/tests/Spout/Reader/XLSX/ReaderTest.php
index c705f2f..3fa6ec1 100644
--- a/tests/Spout/Reader/XLSX/ReaderTest.php
+++ b/tests/Spout/Reader/XLSX/ReaderTest.php
@@ -140,6 +140,21 @@ class ReaderTest extends \PHPUnit_Framework_TestCase
         $this->assertEquals($expectedRows, $allRows);
     }
 
+    /**
+     * @return void
+     */
+    public function testReadShouldSupportFilesWithoutCellReference()
+    {
+        // file where the cell definition does not have a "r" attribute
+        // as in <c r="A1">...</c>
+        $allRows = $this->getAllRowsForFile('sheet_with_missing_cell_reference.xlsx');
+
+        $expectedRows = [
+            ['s1--A1'],
+        ];
+        $this->assertEquals($expectedRows, $allRows);
+    }
+
     /**
      * @return void
      */
diff --git a/tests/resources/xlsx/sheet_with_missing_cell_reference.xlsx b/tests/resources/xlsx/sheet_with_missing_cell_reference.xlsx
new file mode 100644
index 0000000..4e86cda
Binary files /dev/null and b/tests/resources/xlsx/sheet_with_missing_cell_reference.xlsx differ