Reading in CSV files

Hi there. I'm using the following code to read in any number of CSV files into a single worksheet and concatenating them together

File_Path = "H:\pathname"

strName = Dir(File_Path & "\" & "XXXXX*.CSV")  
Do While strName <> vbNullString

    If active_workbook.Name <> strName And strName <> "" Then
        Workbooks.OpenText Filename:=File_Path & "\" & strName, startrow:=1, _
            DataType:=Excel.XlTextParsingType.xlDelimited, _
            TextQualifier:=Excel.XlTextQualifier.xlTextQualifierDoubleQuote, _
            Comma:=True, local:=True
        Set dataset_workbook = ActiveWorkbook
        Range(ActiveCell.SpecialCells(xlLastCell), Cells(1)).Copy
        active_sheet.Activate
        Cells(ActiveCell.SpecialCells(xlLastCell).Row + 1, 1).Select
        ActiveSheet.Paste
        dataset_workbook.Close
    End If
    strName = Dir
Loop

It works fine the first time I run it after opening the workbook (I've got 12 rows of data across 3 CSVs) 12 rows are pasted and 1 blank row at the beginning.

The second time I run it it pastes into the worksheet starting from row 14, and then 27 the third time etc.

Does anyone know a way I can make sure it always pastes starting from row 1?

Thanks in advance.