I see card reader on Ethernet Shield, but I heard somewhere that software of Arduino does not support this one!
Is it true? Can not Arduino use miniSD card reader of Ethernet Shield?
So, I see that exists not official library only. It may be bad.
The original Ethernet Shield had a footprint for a SD card (and some boards actually shipped with a full-sized SD connector soldered onto the board), but the SD part didn't work (for a number of reasons due to unfortunate design decisions).
If your Ethernet Shield has the uSD connector as shown in the picture you posted, it is the new version and you can ignore all of the old rumblings, grumblings and kludgy pseudo-fixes that have appeared here and other places over the years.
Anyhow...
Check out the ladyada Ethernet+SD Tutorial This is for the new version and they say that it works just fine. The tutorial shows how to access SD memory using the SdFat library. Given the excellent track record of ladyada, I believe that it works as shown in that tutorial.
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I don't have one of the new Ethernet Shields to test, but I am following this subject closely.
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Regards,
Dave