Introduction:
A file allocation system is a method used by an operating system to allocate space on a storage device for files. There are several types of file allocation systems, each with its own advantages and disadvantages. The question asks for the type of file allocation system that is not among the given options.

Explanation:
The four types of file allocation systems mentioned in the options are:
a) Contiguous system allocation
b) Non-contiguous system allocation
c) Linked allocation
d) Indexed allocation

Contiguous System Allocation:
In a contiguous system allocation, each file is stored as a contiguous block of data on the storage device. This means that the entire file is stored in a single continuous section of the storage space. This type of allocation provides fast access to the file and is easy to implement. However, it suffers from the limitation that files cannot grow or shrink dynamically, and there may be fragmentation issues.

Non-contiguous System Allocation:
Non-contiguous system allocation, also known as the linked allocation method, allows files to be stored in non-contiguous blocks of data on the storage device. Each block contains a pointer to the next block in the file. This method allows files to grow and shrink dynamically, and it eliminates fragmentation issues. However, it can result in slower access times due to the need to traverse the linked blocks.

Linked Allocation:
Linked allocation is a type of non-contiguous system allocation where each file is divided into blocks that can be scattered across the storage device. Each block contains a pointer to the next block in the file. This method allows files to grow and shrink dynamically, but it can result in slower access times due to the need to traverse the linked blocks.

Indexed Allocation:
Indexed allocation is a type of non-contiguous system allocation where a separate index block is used to store the addresses of the blocks that make up a file. The index block contains pointers to the actual data blocks. This method allows fast access to the file, but it requires additional space for the index block.

Conclusion:
Based on the explanations above, the correct answer is option 'B' - Non-contiguous system allocation. This is because non-contiguous system allocation, also known as linked allocation, is indeed a valid type of file allocation system. Therefore, it should not be considered as the answer to the question.