We present the results of phase- and time-resolved study of iron spectral features in the emission of the Be/X-ray transient pulsar V 0332+53 during its type II outburst in 2004 using archival RXTE/PCA data. Coherent pulsations of both fluorescent iron line at ~6.4 keV and neutral iron K-edge at ~7.1 keV have been detected throughout the entire outburst. The pulsating iron K-edge is reported for the first time for this object. Near the peak of the outburst, the 3-12 keV pulse profile shows two deep, Fmax/Fmin~2, and narrow dips of nearly identical shape, separated by exactly Δϕ=0.5 in phase. The dip spectra are nearly identical to each other and very similar in shape to the spectra outside the dips. The iron K-edge peaks at the phase intervals corresponding to the dips, although its optical depth τK~0.05 is by far insufficient to explain the dips. The iron line shows pulsations with a complex pulse profile without any obvious correlation with the total flux or optical depth of the K-edge. Accounting for the component associated with reprocessing of the pulsar emission by the surface of the donor star and circumstellar material, we find a very high pulsation amplitude of the iron line flux, Fmax/Fmin~10. We demonstrate that these properties of V 0332+53 cannot be explained by contemporary emission models for accreting X-ray pulsars and speculate about the origin of the observed iron spectral features.