A sanitizable signature scheme is a signature scheme which, after the signer generates a valid signature of a message, allows a specific entity (sanitizer) to modify the message for hiding several parts. Existing sanitizable signature schemes require the message to be divided into pre-defined blocks before signing so that each block can be sanitized independently. However, there are cases where the parts of the message which are needed to be sanitized can not be determined in the time of signing. Thus, it is difficult to decide the partition of the blocks in such cases. Since the length of the signature is usually proportional to the number of blocks, signing every bit independently will make the signature too long. In this paper, we propose a solution by introducing a new concept called sequential bitwise sanitizable signature schemes, where any sequence of bits of the signed document can be made sanitizable without pre-defining them, and without increasing the length of signature. We also show that a one-way permutation suffices to get a secure construction, which is theoretically interesting in its own right, since all the other existing schemes are constructed using stronger assumptions.