The quantization based embedding systems are usually used in the information hiding domain, thanks to their efficiency and simplicity. In other hand, they are known to be insecure in steganography context (according to Cachins' security definition) because they distort the stego-signal density function. In this paper, we show that an important kind of quantization based systems (those resulting from the combination with the spread transform and classical data hiding schemes based on quantization ) preserve the probability density function of the stego-signal. We prove the undetectability theoretically and show how the spread transform makes the stego-message statistically non-dectectable in the real case.