Software you will need:

VirtualDubMod

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Start up VirtualDubMod, click "Video" at the top and then click "Direct stream copy". (Screen Shot Below)

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Now go ahead and click "File" at the top, then "Open video file..." and select your first .avi file you wish to join (red) and then click the "Open" button (blue). (Click "NO" if it asks you if you want to rewrite the header) (Screen Shot Below)

After it is loaded, click "File" at the top, then click "Append segment" and select the 2nd avi file or the file you want to join to (red). Repeat this step for each avi file you wish to join. (Screen Shot Below)

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After selecting all of the files you want to join, go ahead and click "File" at the top, then click "Save As..." and type a file name for the final .avi you will produce (red). Then click "Save" (blue) and wait for it to finish. Done! (Screen Shot Below)