We investigate theoretically the relative time delay of photoelectrons originating from different atomic subshells of noble gases. This quantity was measured via attosecond streaking and studied theoretically by Schultze et al (2010 Science 328 1658) for neon. A substantial discrepancy was found between the measured and the calculated values of the relative time delay. Several theoretical studies were put forward to resolve this issue, e.g., by including correlation effects. In the present paper we explore a further aspect, namely the directional dependence of time delay. In contrast to neon, for argon target a strong angular dependence of the time delay is found near the Cooper minimum.