The decomposition of a signal on the sphere with the steerable wavelet constructed from the second Gaussian derivative gives access to the orientation, signed-intensity, and elongation of the signals local features. In the present work, the non-Gaussianity of the WMAP temperature data of the cosmic microwave background (CMB) is analyzed in terms of the first four moments of the statistically isotropic random fields associated with these local morphological measures, at wavelet scales corresponding to angular sizes between 27.5 arcminutes and 30 degrees on the celestial sphere. While no detection is made neither in the orientation analysis nor in the elongation analysis, a strong detection is made in the excess kurtosis of the signed-intensity of the WMAP data. The non-Gaussianity is observed with a significance level below 0.5% at a wavelet scale corresponding to an angular size around 10 degrees, and confirmed at neighbour scales. This supports a previous detection of an excess of kurtosis in the wavelet coefficient of the WMAP data with the axisymmetric Mexican hat wavelet (Vielva et al. 2004). Instrumental noise and foreground emissions are not likely to be at the origin of the excess of kurtosis. Large-scale modulations of the CMB related to some unknown systematics are rejected as possible origins of the detection. The observed non-Gaussianity may therefore probably be imputed to the CMB itself, thereby questioning the basic inflationary scenario upon which the present concordance cosmological model relies. Taking the CMB temperature angular power spectrum of the concordance cosmological model at face value, further analysis also suggests that this non-Gaussianity is not confined to the directions on the celestial sphere with an anomalous signed-intensity.
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