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Let      f : ( C n , 0 ) →  ( C k , 0 ) f:({C^n},0) \to ({C^k},0)       be the germ of an isolated complete intersection singularity. The structure of strata      μ  = const \mu = \operatorname {const}       in a critical set of      f f       is studied. The main result is the following: if the dimension of the stratum      μ  = μ  ( 0 ) \mu = \mu (0)       is      k −  1 k - 1      , then      f f       coincides with a family of hypersurface singularities with constant Milnor number.

The structure of a critical set of a complete intersection singularity