There are many proposals of unkeyed hash functions based on block ciphers. Preneel, Govaerts and Vandewalle, in their CRYPTO’93 paper, presented the general model of unkeyed hash functions based on block ciphers such that the size of the hashcode is equal to the block size and is almost equal to the key size. In this article, it is shown that, for every unkeyed hash function in their model, there exist block ciphers secure against the adaptive chosen plaintext attack such that the unkeyed hash function based on them is not one-way. The proof is constructive: the secure block ciphers are explicitly defined based on which one-way unkeyed hash functions cannot be constructed. Some of the block ciphers presented are secure even against the adaptive chosen plaintext/ciphertext attack.