This paper generalizes the specification of Basic Interval Arithmetic Subroutines (BIAS) to support interval arithmetic on directed (i.e. proper and improper) intervals. This is due to our understanding that the arithmetic involving improper intervals will be increasingly used in future applications and the corresponding interval arithmetic implementations require no additional cost. We extend BIAS specification to be sufficiently precise and complete, to include everything a user needs, such as subroutine s purpose, name, method of invocation and details of its behaviour and communication with the environment. The specified interval arithmetic subroutines for directed intervals are consistent with conventional interval arithmetic and IEEE floating-point arithmetic.