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FORTRAN II was a significant improvement, it added the capability for separate compilation of program modules and introduced subroutines and the common block, amongst other things, assembly language modules could also be 'linked loaded' with FORTRAN modules. FORTRAN II appearing for the 704 in June 1958 and later in the year for the 709 and 650.

FORTRAN III (1958) was never released to the public. It made it possible to use assembly language code right in the middle of the FORTRAN code. Such "inlined" assembly code can be more efficient, but the advantages of an HLL are lost (e.g. portability, ease of use).

FORTRAN IV (1961) was a 'clean up' of FORTRAN II, improving things like the implementation of the COMMON and EQUIVALENCE statements and eliminating some machine-dependant language irregularities.

A FORTRAN II to FORTRAN IV translator was used to retain backward compatibility with earlier FORTRAN programs.

Many non-IBM compilers were produced. This lead to many incompatibilities and restricted portability between systems. These differences lead to growing pressure for standardisation of the language.

In May 1962 an ASA, American Standards Association, committee started developing a standard for the FORTRAN language, a very important step that made it worthwhile for vendors to produce FORTRAN systems for every new computer, and made FORTRAN an even more popular HLL.